Short Answer

Use integration formulas to solve each integral in Exercises 21–62. You may have to use algebra, educated guess- and- check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. (Hint for Exercise 54: $\tan (x) = \frac{\sin (x)}{\cos (x)}$ ).
$\int x^{2} {(x^{3} + 1)}^{5} d x .$

The value of given integral is $\frac{{(x^{3} + 1)}^{6}}{18} + c .$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

Given an integral $\int x^{2} {(x^{3} + 1)}^{5} d x .$

Step 2. Formula involved.

We use substitution method in this integration and then below formula will be used:

$\int x^{n} d x = \frac{x^{n}}{n + 1} + c .$

Step 3. Solving the integral.

$L e t t = x^{3} + 1, d t = 3 x^{2} d x, o r x^{2} d x = \frac{d t}{3} . S u b s i t u t i n g t h i s i n t h e i n t e g r a l w e g e t, \int x^{2} {(x^{3} + 1)}^{5} d x = \int t^{5} \frac{d t}{3} = \frac{1}{3} \int t^{5} d t = \frac{1}{3} \frac{t^{6}}{6} + c = \frac{t^{6}}{18} + c = \frac{{(x^{3} + 1)}^{6}}{18} + c .$

Find Study Materials for

Create Study Materials

Select your language

Calculus

Answers without the blur.

Short Answer

Step by Step Solution

Step 1. Given Information.

Step 2. Formula involved.

Step 3. Solving the integral.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Calculus

Answers without the blur.

Short Answer

Step by Step Solution

Step 1. Given Information.

Step 2. Formula involved.

Step 3. Solving the integral.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths