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Chapter 5: Q. 69 (page 417)

Solve each of the integrals in Exercises 21鈥�70. Some integrals require substitution, and some do not. (Exercise 69 involves a hyperbolic function.)

鈭�xsinhx2dx

Short Answer

Expert verified

The solution of the given integral is 鈭�xsinhx2dx=12coshx2+C.

Step by step solution

01

Step 1. Given Information

Solving the given integrals.

鈭�xsinhx2dx

02

Step 2. Using the substitution method.

u=x2dudx=2xdu=2xdx12du=xdx

03

Step 3. This substitution changes the integral into 

鈭�xsinhx2dx=12鈭�sinhudu鈭�xsinhx2dx=12coshu+C鈭�xsinhx2dx=12coshx2+C

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Most popular questions from this chapter

Solve the integral :鈭�xex2+1dx

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.

For each function u(x) in Exercises 9鈥�12, write the differential du in terms of the differential dx.

u(x)=1x

Solve the integral: 鈭�xlnx2dx

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�9-x2xdx
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