Show that 3x2 +6x +2 = 3 (x+1) - by completing the square. Hence, evaluate the 2 integral dx. V3x? + 6x +2

Q: Evaluate the integral dx 2x x - 3x? 1 V3 + V2 x u- - V7 VX + C 2/3 TV3 1 In 2/3"/7x + V3 +C -In 4…

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Q: Evaluate the integral. V3/2 5x2 dx V1 - x2

A: Consider the trigonometric identities 1)  cos2x = cos2x - sin2x = 1- 2sin2x 2)  cos2x + sin2x = 1 3)…

Q: Evaluate the integral dx (3x + 15)²’ by making the appropriate substitution: u = dx + 15)?

A: To evaluate:∫dx3x+152

Q: Evaluate the integral  dx*(csch(3x))^2

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Q: 7x² dx Vx² – 16 - +C

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

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Q: Evaluate the integral dx 2xx - 3x? A -In 4 V2x + V3 +C 1 V3+ 2x B In +C 2/3 V3-2 +C In 2/3 "/7x + /3…

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Q: Evaluate the integral. V3/2 19x2 dx V1 - x2

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Q: Evaluate the integral. dx Vx2 - 10x + 16

A: Given ∫dxx2-10x+16 ∫dxx2-10x+16=∫dxx2-10x+25-25+16=∫dxx2-10x+25-9=∫dx(x-5)2-9=∫dx(x-5)2-32

Q: -8 1 The integral dx x2 + 64

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Q: 5e3* dx 9-12e3* + 4e6x ,3x 6.

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Q: Evaluate the integral. 3x2 2+ 4x3 dx 2 + 4x-

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Q: Evaluate the integral. | (7x2-6x +7) dx

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Q: Integrate from 0 to 2

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Q: Evaluate the integral. 7x3 dx = Vx2 – 25 +C

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Q: Graph the integrand and use geometry to evaluate the integral. 6 2) s V36 - x2 dx -6

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Q: Evaluate the integral: 9x + 43 -dx = 2x² + 17x – 9

A: Given: I=∫9x+432x2+17x-9dx for evaluating given integral, we substitute 9x+43=944x+17+194 so,…

Q: Evaluate the integral. .V3/2 35x2 dx V1- x2

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Q: Evaluate the Integral 2. S V5 + 12x – 9x²dx - ANSWER: 2. (3x-2)v5+12x-9x²+9Sin¬13*- 2]+C (3х-2)

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Q: 9x2 - 4 dx

A: Given that, Apply u-substitution: Differentiate both sides with respect to x, Plug the values of…

Q: Evaluate the integral dx (8x + 3)3 by making the appropriate substitution: u = 8х + 3 dx (8x + 3)3…

A: Recall:    ∫un du=un+1n+1+c ; where c is an integration constant.

Q: Evaluate the integral 3e2x 2e-2x 1 In vZe-2x + /2e-4x – 3 +C 2/7 - 2x 2/3e2x - 2e-2x+C -등 Arcsinl…

A: Explained below

Q: Solve the integral: Seln(2x²+3x-4)³ (4x+3)dx eln(2x²+3x-4)³ A (2x²+3x-4) (2x²+3x+4)*(4) 3 B + C…

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Q: Evaluate the integral dx (7x + 6)2 by making the appropriate substitution: u = dx (7x + 6)

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Q: ( Evaluate the integral: 64x² – 49 -dx -

A: Given∫64x2-49x3dx

Q: b) Show that 2x² + 8x + 14 = 2 (x + 2)° +3 by completing the square. Hence, evaluate the integral-…

A: Use integration rules

Q: Show that L₁J - dx x² + 2x + 2 = In(√5-2).

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Q: Show that 2x2 +8x+14=2(x+2} +3| by completing the square. Hence, evaluate the V3 (x+2/2x? integral |…

A: Given that: ∫3(x+2)2x2+8x+14dx

Q: Evaluate the integral. V36 – x² dx = 18sin- +xV36 – x² + c V36 – x² dx = 36sin--xV36 – x² + C / V36…

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Q: 10. Using the substitution u 2x - 1, prove that %3D 3 8 dx J1 (2x-1) 25

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Q: SxVx² √x² - 4 dx

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Q: Find the general solution to the DE using the method of Variation of Parameters: у" - Зу" + Зу'…

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Q: Evaluate the integral 7-2x dx /7+12x-4x²

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Q: Evaluate the integral dx (2x + 4)* by making the appropriate substitution: u = dx (2x + 4)°

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Q: Calculate the integral. 2x° (x + 2)²dæ

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Q: Evaluate the integral. 5x2 +3x- Vx - 2 dx 5.

A: topic - definite integration

Q: Evaluate the integral. 2. (9x2 - 8x + 6) dx

A: the Integration is a process of finding the anti derivative of a function. There are basically two…

Q: Solve the integral: eln(2x²+3 +3x-4)³( (4x + 3)dx (2x²+3x+4)² + C A 4 (2x²+3x+4)*(4) 3 + C eIn(2x² +…

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Q: 10х> — 5х For the integral -dx , if u = x*-x2+6 then Mdu = (10x³-5x)dx, what is %3D x4-x²+6 M?

A: We have integral ∫10x3-5xx4-x2+6dxifu=x4-x2+6

Q: E valvate cox³ (x²+3)dx 2.

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Q: Solve the integral: Seln(2x² + 3x −4)³ (4x + 3)dx eln(2x² + 3x-4)³ (4x+3) 3(2x²+3x-4) A + C…

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Q: Evaluate the integral. dx xV 49x2 - 6

A: Given that: ∫dxx49x2-6

Q: b) Show that 2x2 +8x +14 2(x+2) +3 by completing the square. Hence, evaluate the integral dx. (x…

A: Given that: ∫3(x+2)2x2+8x+14dx

Q: Use the method of completing the square to evaluate the integral. 2x + 1 dp- x + 2x+ 17

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Q: Find the integral. [(3 - 7x° + 5) dx 7 OA. 9x° -**5 7x* +5x +C O B. °-** 7 + 5x +C OB. Oc. 9x°. -**…

A: According to the properties of integration we have: ∫[f(x)±g(x)] dx=∫f(x) dx ± ∫g(x) dx

Q: Evaluate the integral: –(9z²+7x) dr %3D (1-1)(z+1)²

A: Given :∫-(9x2+7x)(x-1)(x+1)2dx

Q: Evaluate the integral dx 2x3 - 3x x |/3x - /2 2/2"V3x + v2 1 +C O 16V2 + V3 In 3 |/2 - 3x +C In +C…

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Q: Prove that: 3-4x² dx 4VIn3

A: The given integral is I=∫0∞3-4x2dx. The idea is to evaluate the above integral using gamma function.…