7) Evaluate: S(-x² + 4x – 1)dx

Q: Evaluate the integral. X-7 dx X-7 dx = 8 %3D

A:

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

A: To evaluate:∫dx3x+152

Q: 20. Use u substitution to evaluate. S secrtant 1+secx dx

A: Evaluation of the indefinite integral by substitution method

Q: Evaluate the integral dx (5x + 9)* by making the appropriate substitution: u = dx (5x + 9)*

A:

Q: Evaluate the integral x3 + 39 dx. + 4x + 3 x2

A: Try to simplify the numerator in terms of the denominator.

Q: (a) By using the substitution, u = 1 + x*, or otherwise, find x3 -dx 1+ x4

A:

Q: Evaluate the integral. 8. 9. dx x² 7.

A:

Q: 3. 9. dx Sx+I

A:

Q: 5 (show resulting de) 2xdx - dy=x(xdy - 2ydx) When: x= -3 , y = 1 %3D

A: Differential equation and it's solution

Q: Find the integral. |(2x° – 7x° + 5) dx 1 A. 3 7 4 x* + 5x + C 4

A: he given integral is ∫2x5-7x3+5dx

Q: Evaluate the integral 2 dx where fx) if -2 s xs 0 16-2 if 0xs3

A: Given function is The integral isThe integral can be written as: Plugging the function and applying…

Q: 1. fx³ In x dx

A: Evaluate the integral equation by integration by parts .

Q: evaluate the integral.

A:

Q: Find the integral. dx 7/3-3x2 +C O b 2x2 육x기3-2x-2.c O d + 2x

A:

Q: Evaluate the integral (2х — 8)dx х2 — 6х + 18

A: We know that integration power rule is - Integration of xn is xn+1/n+1+ C  Here C is integration…

Q: d Verify coth x = - csch² x. dx

A: Differentiation is the rate of change of some variable with respect to the other variable. If a…

Q: 4 – 2x dx. x3 + 2x2

A:

Q: o evaluate (In x)² +3 dx,

A: answer is in next step  option C is correct

Q: 3x 2.5 dx V1 — 5х2

A:

Q: sec2 X dx 3

A:

Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: The given integral is ∫2 dxx1+lnx2 Find your answer below

Q: 4х-6 -dx х2-8х+20

A:

Q: evaluate using the appropriate method or combination of methods.

A:

Q: 4 8 + x2 dx /1

A:

Q: 8. Compute using the trig. substitution S x2 -dx (1–x²)1/2

A:

Q: Solve using product rule d(uv) = u dv + v du: f(x) = (x^2 + 4) (x^4 – 4x^2 + 16)

A: Given that, fx=x2+4x4-4x2+16 Differentiation formulae: ddxuv=uddxv+vddxu    [Product rule]…

Q: O f(3x² + sec² 2x) dx

A: Given query is to find integral.

Q: の dy Sーメ+ リーX +5

A: This is a problem related to differential equation. Based on the general formula we will solve the…

Q: 1 y = -e*(dsin²3x-tanx ³) y'=? 10 (fx +1)

A:

Q: a) dt 9 =dx xVln x b)

A:

Q: 3 5 8x 15 dx 5 x4 |

A:

Q: 2. Evaluate the integral: 2xe-**dx -0

A: topic - integration

Q: What change of variables would you use for the integral  ∫(4 - 7x)-6 dx?

A: Consider the following integral: I=∫4-7x-6dx Substitute 4-7x=t→-7dx=dt→dx=-17dt in I:…

Q: If In(ax)dx = 4, then a ( In(ax)dx %3D 1 4

A: we have to find the value of a

Q: Evaluate az+1)in(d.r+1)dr. 1 dx.

A: The integration function is ∫14x+1ln4x+1dx

Q: Evaluate the integral. (3x2 9) dx

A:

Q: 13. Use a u-substitution to evaluate /x²/(x³ – 2) dx

A:

Q: 6. Evaluate the integral dx (4x2 + 1)(x² + 4)

A:

Q: Evaluate the integral (2х + 6)dx х2 — 2х + 17

A:

Q: 4. Prove 1 < | V1+ a dx <2 0,

A:

Q: To evaluate the integral/ V3 – 3x² dx,

A: Substitute, x=sin(θ)dx=cosθ dθ The expression f(x) becomes,

Q: 4. Prove that ах x" ea" dx xn- п-1 ‚ax dx а а

A:

Q: - 7x)4 dx Using an appropriate substitution, evaluate: B

A: The given integral: I=∫x6-7x4 dx

Q: 10 Evaluate the integral f 2x (x2 + 4) " dx using the substitution u = x² + 4. 2x (x² + 4)*" dx =|…

A: The given integral ∫2xx2+410dx

Q: Evaluate the integral. "4 4 + x² dx

A: We have to find the integral

Q: 5. prove that d (-x) (+ x) = X dx dx d² dx² - x² +1

A:

Q: 16. Evaluate x + v1- x² dx by interpreting it in terms of areas.

A:

Q: find using Serie s リ2 dx "I+X 2

A: As a first step, we need to obtain a series for the integrand.

Q: 2x²-3x + 10 dx (x²+4)2

A: The objective of the question is evaluate the indefinite integral.