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Chapter 5: Q 37. (page 429)

Solve the integral:鈭�3xex2dx

Short Answer

Expert verified

The required answer is32ex2+c.

Step by step solution

01

Step 1. Given information. 

We have given integral is鈭�3xex2dx.

02

Step 2. Solve the integration by parts . 

We have,

u=x2du=2xdxdu2=xdx

The formula of integration by parts is 鈭�udv=uv-鈭�vdu

鈭�3xex2dx=3鈭�xex2dx=312鈭�ex2dx=32ex2+c

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Most popular questions from this chapter

Find three integrals in Exercises 39鈥�74 that can be solved without using trigonometric substitution.

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.

Why doesn鈥檛 the definite integral鈭�231-x2dx make sense? (Hint: Think about domains.)

Find three integrals in Exercises 27鈥�70 for which a good strategy is to apply integration by parts twice.

Show by differentiating (and then using algebra) that 鈭�cot鈦�sin鈭�1鈦�xand 鈭�1鈭�x2xare both antiderivatives of 1x21鈭�x2. How can these two very different-looking functions be an antiderivative of the same function?
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