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Chapter 5: Q. 49 (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�ex2鈭�exdx

Short Answer

Expert verified

The solution of the given integral is 鈭�ex2鈭�exdx=鈭�ln2鈭�ex+C.

Step by step solution

01

Step 1. Given Information 

Solving the given integrals.

鈭�ex2鈭�exdx

02

Step 2. Solving the given integral using substitution method. 

Let

u=2鈭�exdudx=鈭�exdu=鈭�exdx鈭�du=exdx

03

Step 3. This substitution changes the integral into  

鈭�ex2鈭�exdx=鈭�鈭�1udu鈭�ex2鈭�exdx=鈭�lnu+C鈭�ex2鈭�exdx=鈭�ln2鈭�ex+C

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Most popular questions from this chapter

Solve 鈭�x+2x2+4x32dxthe following two ways:

(a) with the substitution u=x2+4x;

(b) by completing the square and then applying the trigonometric substitution x + 2 = 2 sec u.

Solve given definite integral.

鈭�35鈥�x2鈭�9dx

Suppose you use polynomial long division to divide p(x) by q(x), and after doing your calculations you end up with the polynomial x2-x+3 as the quotient above the top line, and the polynomial 3x 鈭� 1 at the bottom as the remainder. Thenp(x)=___andp(x)q(x)=____

Solve given integrals by using polynomial long division to rewrite the integrand. This is one way that you can sometimes avoid using trigonometric substitution; moreover, sometimes it works when trigonometric substitution does not apply.

鈭�x4-32+3x2dx

Solve the integral:鈭�x2e3xdx.
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