e) ſ Vtan x · sec4x dx f) S cos Vx dx

Q: Use a table of integrals to find the indefinite integral.

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: Evaluate the following indefinite integral. dx 21 dx = %3D

A: Concept : ∫xmdx = xm+1m+1 given ∫x·x21dx = ?

Q: sec 0 tan 0 cos(sec 0) d0

A:

Q: | cos(In x) dx

A:

Q: tan³ (2x) dx J cos4(2x)

A: Consider the indefinite integral  ∫tan32xcos4(2x)dx To evaluate the integral, first rewrite it using…

Q: Use any method to evaluate the integrals ∫cot x/cos2 x dx

A:

Q: Evaluate the integral.  integral  cot  3 x   dx

A: Consider the given indefinite integral: Here the objective is to find the indefinite integral of…

Q: Evaluate the integrals using integration by parts. ∫tan-1 y dy

A:

Q: (x²-x)dx

A:

Q: Bx x+2 e t e de

A: Given ∫e3x+e-x2ex+2dx

Q: ( (x? + 1)e* dx

A: Given

Q: Use the Table of Integrals to evaluate the integral.  ∫ x Sin( x2) Cos (3 x2 )dx

A:

Q: Evaluate the integrals ∫cos3 x sin x dx

A:

Q: dx V1– 18x?

A: To evaluate the given integral.

Q: |1+cos ydy

A: Let I=∫1+cosy dy

Q: S sin x e cosxdx

A: The objective of the question is evaluate the given indefinite integral using substitution method.

Q: | (3x – 2)2 dx.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Evaluate the following indefinite integrals using integration by trigonometric substitution.…

A:

Q: x3 sin(x) dx

A: Solve by integration by parts

Q: Determine the following indefinite integral. 1 dx

A:

Q: Find the integral. (Use C for the constant of integration.) sin(-3x)cos(2x) dx

A:

Q: Evaluate the integral. TC cos(x) sinh(x) dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) sin(8x) cos(5x) dx

A:

Q: ydy V16–9y* 4

A:

Q: Use Simpson’s Rule with n= 10 to approximate the integral 0 to 1 e x2   dx

A: Given: n=10I=∫01ex2dx

Q: Consider the following integral: sinx dxdy By reversing the order of integration, the value ofI is…

A: Given limits- y<x<π0<y<π

Q: 4. Calculate the integral, f 4e" sinh x dx.

A:

Q: Evaluate the integrals ∫sin x cos x dx

A: Given: The integration∫sinxcosxdx, To Evaluate: The given indefinite integration.

Q: Use integration tables to find or evaluate the integral.

A: To evaluate: ∫01x1+ex2dx Evaluating the given integral, Let substitute  t=x2 dtdx=2xdt2=xdx…

Q: /2) dx

A:

Q: Find the trigonometric integral. (Use C for the constant of integration.) sin(x) cos os°(x) dx

A:

Q: Find or evaluate the integral using substitution first, then using integration by parts. cos(In x)…

A:

Q: Evaluate the integrals using integration by parts. ∫t2 cos t dt

A:

Q: Evaluate the integral. integral 0  to pie /2    cos x + sin x dx

A:

Q: dx 17. 2 18+4x-4r² |

A: We will solve the problem.

Q: Solve the following integral using integration by parts: In finx dx √x

A: To evaluate the given integral∫ln(x)xdx using integration by parts.

Q: Evaluate the following integrals using integration by parts method: x sin 2x dx

A:

Q: tan Įx sec² įx dz. x³ + 3x dx. x2 + 1

A: LetI=∫x3+3xx2+1dxI=∫x(x2+3)x2+1dxPu x2+1=ux2=u-1differentiate 2xdx=duxdx=du2I=∫(u-1+3)udu2Take the…

Q: 18. | V4 - х? dx

A:

Q: Determine the following indefinite integral.

A:

Q: Use integration by parts to evaluate the definite integral. e2x sin x dx

A:

Q: |cos' y sin' ydy cos³ sin’ ydy

A: Strip out one cosine and write everything else in terms of the sine, using the formula…

Q: Evaluate the following integral using integration by parts. x¹ ln x dx

A: This question is based on integration by parts.

Q: Evaluate the following definite integral by using the method of integration by parts. x In(x) dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) cos−1(x) dx

A: Use the method for integration by parts to determine the given integral. I=∫cos−1xdxLet…

Q: Apply integration by parts to find the indefinite integral. S e2t cos(3t)dt

A:

Q: Use Simpson's rule to approximate the following integrals: (using n= 8 subintervals) a. f, cos x³ dx…

A: We have the formula for Simpson's rule…

Q: Evaluate the integral. (Use C for the constant of integration.) cos(x) (4 + 8 sin²(x)) dx

A: Solve the intregal

Q: Evaluate the following improper integral. If it diverges, then type 'DNE. Otherwise, find its exact…

A: The given integral,           ∫015238-38x2dx

Q: Evaluate the integrals using integration by parts. ∫θ cos πθ dθ

A: Given: ∫θcosπθdθ