Consider the integral dx, (x² + a²)³/2 where a is a positive real number.

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A:

Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

A: Given information: Concept Used:

Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A: Consider the integration ∫x3x2+9dx Substitute x=3tanθ ⇒dx=3sec2θdθ Hence,…

Q: Evaluating the integral f In(r³)dx, where x > 0 yields:

A:

Q: Evaluate the integral :(x² + y* )dzc>xcy = ?

A:

Q: Evaluate the integral. 17 dx 2 Vx² – 1 - NOTE: Enter the exact, fully simplified answer.

A: Let's find.

Q: 1e uex dx (3+x²)5/2 x3 Ue be

A: ∫03x33+x252 dx Consider, ∫x33+x252 dx Put, x=3 tanθ⇒1=3 sec2θ·dθdx⇒dx=3 sec2θ dθ Therefore,…

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 9e dx 1+e2=…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) | 3x2 cos(mx) dx

A:

Q: Evaluate the integral by making the given substitution.

A:

Q: Using an appropriate substitution, 8tan-1x the integral J dx equals: 1+x2

A:

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral In(x) dx…

A: We use trapezoidal rule ,midpoint rule,simpson's rule to approximate the given integral

Q: 2x dx ,(x2 +1)2 - 00

A:

Q: Use a substitution to change the integral into one found in the table of integrals, then evaluate:…

A:

Q: 3 9-x 1 dy dx dz V9-2? (x² + y²)1/2 3

A:

Q: Evaluate the integral. (Use C for the constant of i 4x2 + 3x + 4 dx (x² + 1)2

A:

Q: let b be a constant. use definition to find  (integral 0 to b)(x+1)^2 dx.

A: Given: The expression of integral as ∫0bx+12dx, where b is a constant, To evaluate: The value of…

Q: Make the substitution u = and evaluate the resulting definite integral. +oo dx = V7x

A:

Q: Evaluate the integral. (Use C for the constant of integration.) | sin (0) cos (@) de

A: Given integral, ∫sin3θ cos6θ dθ It can be written as =∫sin2θ sinθ cos6θ dθ=∫1-cos2θ sinθ cos6θ…

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. dy dx - x²

A: NOTE: Refresh your page if you can't see any equations. .

Q: Consider the indefinite integral 5x+6 dx: a) This can be transformed into a basic integral by…

A: Given ∫e5x+6 dxLet u=5x+6 →dudx=5→dx=15du

Q: In Exercises , use a substitution to change the integral into one you can find in the table. Then…

A: 27. Given integral is, ∫x3+x+1x2+12dx.   It is integrated as follows:

Q: Use the indicated substitution to evaluate the integral.

A: Given:           ∫012x21−x2dx,  x=sinθ

Q: Evaluate the integral. Express answer as both exact and using 2-decimal places. • T X 4 S 2cos X…

A:

Q: Evaluate the integral using an appropriate substitution. dx = +C x√√8-xd

A:

Q: Use Gauss-Legendre formula to evaluate the integral e¯x*dx_with n = 3.

A: Evaluate the integral          ∫01ex2dx using Gauss-Legendre formula with n=3.

Q: Evaluate the integral: fé 2a sec e da

A: Given integral, ∫e2a sece2a  da

Q: Consider the integral dx x . Using u-substitution, what is an appropriate u and du? -2x 2e

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dx,…

A:

Q: Use the substitution a 3 sin t to evaluate the integral f V9 – x² dx.

A:

Q: Evaluate the integral. x sec?(8x) da +C

A:

Q: Evaluate the integral by any method. Enter the exact answer. y2 dy = V9 – 8y

A: The integral is ∫01y29-8ydy Use substitutions to solve the integral. Calculate the exact answer.

Q: Evaluate the integral in terms of inverse hyperbolic function x2 dx Vx² + 1

A: for a part see 2nd,3rd and 4th step. for b part

Q: Evaluate the indefinite integral: dx = +C. %3D

A:

Q: Evaluate the integral.

A: ∫x24-x232dx Put, x=2sinθ⇒1=2cosθ·dθdx⇒dx=2cosθ·dθ

Q: Use the substitution x = 3 sin t to evaluate the integral f v9 – x² dx. - Note: Use C for an…

A:

Q: calculate the integral in terms of the inverse hyperbolic functions.

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: We have to solve the problem

Q: V9x² – 25 53. dx, x > 3 +3

A: consider I= ∫9x2-25x3 dx

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) |…

A:

Q: Evaluate the integral: T So sin(x)dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) cos (a) da J Vsin(a)

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) + 9…

A:

Q: Use the specifie substitution to find or evaluate the Integral. (Use C for the constant of…

A: To solve the integration uisng substitution method

Q: calculate the integral in terms of the inverse hyperbolic functions.

A:

Q: Evaluate the integral F(= - 0)"dz, (x³ by making the appropriate substitution: u = P(* - 0)"de -…

A: NOTE: Refresh your page if you can't see any equations. . ...............(1) substitute…

Q: Evaluate the integral f v96 + 16x² dx using trigonometric substitution.

A:

Q: Use the specified substitution to find or evaluate the integral. (Use C for the constant of…

A: See attached file for a step by step explanation to find the required Integral.

Q: The resulting integral of form --F(0) +C. de has the What should be the value of e to make F(@)=0?

A: