Evaluate the integrals in Exercises 31-3v. Some integrals do not require integration by parts. cos Vx dx sec x² dx 32. 31. Vx x (In x)² dx 33. dx 34. x (In x)² “t *(In x)³ In x dx x? 35. 36. dx х 37. dx 38. dx x³Vx² + 1 dx x² sin x³ dx 40. 41. 42. sin 2x cos 4x dx sin 3x cos 2x dx eVã dx Vx In x dx 43. 44.

Q: In(x) dx Vx

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Q: S. 14 V1 + 7x dx

A:

Q: Suppose f(x, y) = x" + y*. Find fa(1, 1), f,(1, 1), and fz (x, y)

A: Given :f(x,y)=xy+yx

Q: integral by part x² dx

A: Given that  The integral is

Q: (x-7) dx 19. SJ5-4x-x2

A: Answer is following.

Q: dx V (1+ Vx)

A: Since you have asked multiple questions, according to our company guidelines we are supposed to…

Q: 2 1 æ sec-(x) dx 2/V3

A: By see this solution below

Q: 1. | x cos x dx

A: 1 We have to evaluate the integral ∫xcosxdx. Use formula ∫fxgxdx=fx∫gxdx−∫dfxdx⋅∫gxdxdx Here, fx=x…

Q: Integrate tan -1 x dx without using integration by parts.

A: We will find the solution in the following step.

Q: 4x³ (1 - 4x²) 1²/1 2 S- -dx

A:

Q: QUESTION 2 a) Evaluate the integral | dx (x-5) +5 b) Show that 5+4x - x² = 9-(x-2) by completing the…

A: (a). From the given problem: I=∫5x-52+5dx   ...1 Let, u=x-5So,ddxu=ddxx-5dudx=1-0du=dx

Q: 3. (x²+x+4) dx

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Q: Find /- tan- x -dx using integration by parts. x2 ITM

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Q: (a) Evaluate xe* dx using substitution method. (b) Evaluate | 6xe* dx using integration by part…

A: We will find out the required value.

Q: 4 Use Gaussian Integration (4-point form) to approximate x2sin(x)dx

A: Using 4-point formula the given integration is solved.

Q: x+1 Find the indefinite integral: /: dx Vx3+3x

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Q: Numerical Integration: 5 (2x² – 3x) dx 2. 2

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Q: 7sin 2x cot(2x) sin(2x) dx

A: To evaluate the given integral

Q: Hwy find the integration 3 Se vadv V 1-

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Q: Solve the integral equation y =2+

A: Here we use Leibniz Rule .