Evaluate the integral using integration by parts where possible. (Use C for the constant of integration.) | (x² - 9)e2x dx 1. C+(2,² – 2r – x – 17) x(x + 4)6 dx x(x + 4)6 dx 1(r+4)7

Q: r5x³ + 3x² – 2x – 4 dx Consider the indefinite integral x2 – 1 Then the integrand decomposes into…

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Q: dx 6. Evaluate the improper integral. x² +3x+ 2

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Q: A. Evaluate the ff. integrals. Specify what technique you are using. 1) fx² In 2x dx 2) Sxtan-1x dx…

A: Note: As per the company's policy we are supposed to solve only 3 subparts of the question. So…

Q: If 9. 10 f(2)dæ = /: | F(2)dx - / f(x)dæ, f(x)dx + %3| 3 9, what are the bounds of integration for…

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Q: Show the similarity 1 (x² + a²)m dx = 2(-m+1)(x² + a²)m-1 using the substitution u=x^2+ a^2. Also…

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Q: Consider the integral ∫31 ∫1-1(2y2 + xy) dy dx. State the variable of integration in the first…

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Q: b) - Demonstrate the repeated use of integration by parts by proving the reduction formula п-1 S…

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Q: 15x²x³43x - 19 The integral f S can be rewritten as (x + 1)²(x² - 6x + 13) Ax + B C D Slax + + ax² +…

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Q: x³ + 6x² + x +2 fx-1 ax + In{(x + 1)*(x² – x + 1)| +- 2 Tan Ve The resulting integral of -1 + C,…

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Q: 4- 2x Evaluate the following integral : dx 2x +4,

A: The answer is π/3.

Q: dx integralini hesaplayınız. 1-x3

A: Evaluation of integral

Q: 5x (x² +a) dx is In +eTan-1X The resulting integral of + C, where a, b, d, and e are integers. What…

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Q: 2.) Evalvate the Integral ودل أاد-ل (x² _33² dx, .3 2 by making w - x²-3 NOTE: Answer should be in…

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Q: = x2, dv = xe*, and use a substitution to find v from dv. Use C Use integration by parts to find the…

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Q: 1. ſ (x-1)dx x2+5x+6

A: The given integration is ∫(x-1)x2+5x+6 dx  We have to find the integration for the given integral

Q: (6x³ + 3x? x² – 16 89x – 52 dx Consider the indefinite integral Then the integrand decomposes into…

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Q: x'dx use the residual method to calculate the integral (x² +1)(x² +4)

A: Final answer is π/6

Q: Consider V /3x² + 3y²dxdy The integral cannot be solved analytically using basic integration…

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Q: Using Gaussian integration, the integral f(x) dx is equal to? (a) 2 f¹, f(2x + 3) dx (b) f¹ f(2x +…

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Q: If -2 5 [° f(x)dx = [__ * f(x)dx + [_^¸ ƒ(a)dx − [¯* f(x)dx, -8 what are the bounds of integration…

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Q: Consider the functions given.Evaluate the integrals

A: given: ∫16f(x)dx=10∫16g(x)dx=5∫46f(x)dx=5∫14g(x)dx=2 to evaluate ∫468g(x)dx

Q: |(x² + a) 5 5x The resulting integral of dx is In +eTan-1X + C, where a, b, d, and e are integers.…

A: Given:        ∫5xx3+x2+4x+4dx Apply linearity:     =5∫xx3+x2+4x+4dx Factor the denominator:…

Q: If 8 10 | f(2)dæ = f(2)da + I f(æ)dx - / f(x)dx, 4 8, 4 what are the bounds of integration for the…

A: Given information:-

Q: Кр хр (x³y-xy) dx dy anoigand 8.

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Q: 6.2.24. Evaluate the integral. using integration by parts integrate 1 to 2 xln(x) dx   I am unable…

A: Use integral by part rule.

Q: Reverse the order of integration in the following integral. 7 14-2x !! f(x.y) dy dx y14-2 Reverse…

A: From the given integral; I=∫07∫014-2xfx,ydydx Now find the x-intercept and y-intercept.…

Q: (3x³ + 5æ² 5х — 14 dx Consider the indefinite integral x2 4 Then the integrand decomposes into the…

A: Here we use the partial fractionsee below the answer

Q: 2e Evaluate the integral dx 2x +3

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Q: 7x Evaluate the definite integral : dx (6x2+2)2

A: Given,          ∫017x6x2+252dx

Q: 3. The integration of x e* with respect to x is: A. e2x. В. 2хе* С. 2

A: To integrate  xex2 with respect to x: ∫ xex2dx Apply u-substitution: u=x2 Differentiate both sides:…

Q: 5x Q5 integral Evaluate the in dx (x²+1)(2.x-2)

A: Let I=⇃5xx2+12x-2.dx    I=⇃52xx2+1x-1.dxBy Method of partial fractions…

Q: Зx2 — 4х — 9 A + х — 2 Evaluate the integral J x³ – 2x² – 9x + 18 dx using + х — 3 x + 3

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Q: dx a) Evaluate the integral / z In(4x) using the substitution u = In(4x). dx x In(4x) +C b) Evaluate…

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Q: 5x dx. - 6 Compute the integral x2

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Q: Q2/Evaluate the integral: 1.57 9-x2 dy dx x, by changing the order of integration.

A: The integration order can be changed by changing the inner integral to outer and outer integral to…

Q: (5x° + 4x + Ix Consider the indefinite integral dx x2 – 1 Then the integrand decomposes into the…

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Q: S For x1/2 x−x³ dx and using the substitution u=x1/2, the resulting integral takes the form:

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Q: 3x3-7x+1 dx # 2) Evaluate the integral X-2

A: As you have asked to solve #2) we will solve only #2).The given integral:∫3x3-7x2+1x-2dxWe will…

Q: 1. Compute the given integral. Using Substitution Method 5x-12 dx = +C 5x2-24x-1 *

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Q: Evaluate the integral. 고-36 x² – 36 . 6cos- (승) +0 /x² – 36 - dx = Vx² – 36 – 6cos¬! + C x² – 36…

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Q: 6x³ + 3x² – 89x 52 dx Consider the indefinite integral x² – 16 Then the integrand decomposes into…

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Q: d.x (a) Evaluate the integral ; x In(4x) using the substitution u = In(4x). dx J r In(4x) +C -7x (b)…

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Q: Evaluate the integral. dx i. 2 x²Vx2–1°

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Q: Using Gaussian integration, (a) 2 ¹₁ f(2x + 3) dx (c) 3 ¹₁ f(3x + 2) dx the integral ff(x) dx is…

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Q: Q2/ Evaluate the integral: 1.57 9-х2 dy dx X. by changing the order of integration.

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Q: 1 (x² +a) b dx is In 5x The resulting integral of +eTan-1 + C, where a, b, d, and e are integers. x³…

A: Given:∫5xx3+x2+4x+4dx= ln⁡x2+a1bx+d+eTan−1⁡x2+C Let, I=∫5xx3+x2+4x+4dx ⇒I=∫5xx2(x+1)+4(x+1)dx…

Q: x³ + 6x² + x+2 s ax + In[cx + 1}*(x² – x + 1)°| + fx-1 Tan-1. V3 The resulting integral of x³ +1 +…

A: use simple integration formula.

Q: 1 (a) for e³x+4 dx Evaluate the following integrals using an appropriate method: (b) √ (3a² +…

A: Given,∫01e3x+4dxLetI=∫01e3x+4dxPut 3x+4=uDifferentiate3dx=dudx=du3As x→0 then u→4As x→1 then…

Q: 5x |(x²+ a) The resulting integral of dx is In +eTan-1X + C, where a, b, d, and e are integers. What…

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Q: (7Vx2 7V22-9 6. Evaluate the integral: dx x4

A: Given that I=∫7x2-9x4 We can use the substitution technique.