Q. 50 Solve each of the integrals in E... [FREE SOLUTION]

Chapter 5: Q. 50 (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.)
$鈭� (x^{2} + 1) \sqrt{x} d x$

Short Answer

Expert verified

The solution of the given integral is $鈭� (x^{2} + 1) \sqrt{x} d x = \frac{2}{7} x^{7 / 2} + \frac{2}{3} x^{3 / 2} + C$ .

Step by step solution

Step 1. Given Information

Solving the given integrals.

$鈭� (x^{2} + 1) \sqrt{x} d x$

Step 2. Simplifying the given integral.

$鈭� (x^{2} + 1) \sqrt{x} d x = 鈭� (x^{2} + 1) x^{1 / 2} d x 鈭� (x^{2} + 1) \sqrt{x} d x = 鈭� (x^{2} 路 x^{1 / 2} + 1 路 x^{1 / 2}) d x 鈭� (x^{2} + 1) \sqrt{x} d x = 鈭� (x^{2 + 1 / 2} + x^{1 / 2}) d x 鈭� (x^{2} + 1) \sqrt{x} d x = 鈭� (x^{5 / 2} + x^{1 / 2}) d x$

Step 3. After simplification.

$鈭� (x^{2} + 1) \sqrt{x} d x = 鈭� x^{5 / 2} d x + 鈭� x^{1 / 2} d x 鈭� (x^{2} + 1) \sqrt{x} d x = [\frac{x^{5 / 2 + 1}}{5 / 2 + 1}] + [\frac{x^{1 / 2 + 1}}{1 / 2 + 1}] + C 鈭� (x^{2} + 1) \sqrt{x} d x = [\frac{x^{7 / 2}}{7 / 2}] + [\frac{x^{3 / 2}}{3 / 2}] + C 鈭� (x^{2} + 1) \sqrt{x} d x = \frac{2}{7} x^{7 / 2} + \frac{2}{3} x^{3 / 2} + C$

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91影视

Solve each of the integrals in Exercises 21鈥�70. Some integrals require substitution, and some do not. (Exercise 69 involves a hyperbolic function.)
$鈭� (x^{2} + 1) \sqrt{x} d x$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Simplifying the given integral.

Step 3. After simplification.

One App. One Place for Learning.

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91影视

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�(x2+1)xdx

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Simplifying the given integral.

Step 3. After simplification.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each of the integrals in Exercises 21鈥�70. Some integrals require substitution, and some do not. (Exercise 69 involves a hyperbolic function.)
$鈭� (x^{2} + 1) \sqrt{x} d x$