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Chapter 5: Q. 72 (page 465)

Solve each of the integrals in Exercises 39鈥�74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
鈭�e2x1-e4x3/2dx

Short Answer

Expert verified

The value of integral is13e2x+132+C

Step by step solution

01

Step 1. Given information

An expression is given as鈭�e2x1-e4x3/2dx

02

Step 2. Solving integrals

Let

u=e2x+1du=2e2xdx

Now substitute the value and simplify as,

鈭�e2xe2x+1dx=鈭�u2du=12鈭�udu=(u)322=13e2x+132+C

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Most popular questions from this chapter

Consider the integral 鈭�x(x2鈭�1)2dx.

(a) Solve this integral by using u-substitution.

(b) Solve the integral another way, using algebra to multiply out the integrand first.

(c) How must your two answers be related? Use algebra to prove this relationship.

Problem Zero: Read the section and make your own summary of the material.

Explain why, if x=asinu, then a2鈭�x2=acosu. Your explanation should include a discussion of domains and absolute values.

Solve given definite integral.

鈭�鈭�11鈥�x39x2鈭�1dx

Solve the integral:鈭�x2e3xdx.
See all solutions

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