Chapter 5: Q 5 2 (page 429)

Solve the integral: $鈭� x^{5} \cos x^{3} d x$

Short Answer

Expert verified

The required answer is $\frac{x^{3}}{3} \sin (x^{3}) + \frac{1}{3} \cos (x^{3}) + c$ .

Step by step solution

Step 1. Given information.

We have given integral is $鈭� x^{5} \cos x^{3} d x$ .

Step 2. Solve the integration by parts .

We have,

$u = x^{3} d u = 3 x^{2}$

The integration is

$鈭� \frac{u}{3} \cos (u) d u = \frac{1}{3} 鈭� u \cos u d u$

Now, $w = u d w = d u$

and

$d v = \cos u d u v = 鈭� \cos u d u v = \sin u$

The formula of integration by parts is $鈭� u d v = u v - 鈭� v d u$ .

$\frac{1}{3} 鈭� u \cos u d u = \frac{1}{3} (u \sin u - 鈭� \sin u d u) = \frac{u}{3} \sin u - \frac{1}{3} (- \cos u) + c = \frac{x^{3}}{3} \sin x^{3} - \frac{1}{3} (- \cos x^{3}) + c = \frac{x^{3}}{3} \sin x^{3} + \frac{1}{3} \cos x^{3} + c$

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91影视

Solve the integral: $鈭� x^{5} \cos x^{3} d x$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the integration by parts .

One App. One Place for Learning.

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91影视

Solve the integral:鈭�x5cosx3dx

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the integration by parts .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Discrete Mathematics

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Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve the integral: $鈭� x^{5} \cos x^{3} d x$