Q. 15 Find three integrals in Exercise... [FREE SOLUTION]

Chapter 5: Q. 15 (page 417)

Find three integrals in Exercises 21鈥�70 that we can anti-differentiate immediately after algebraic simplification.

Short Answer

Expert verified

The three integrals in Exercises 21鈥�70 that we can anti-differentiate immediately after algebraic simplification are $鈭� \frac{\sqrt{x} + 1}{x} d x, 鈭� x^{4} {(x^{3} + 1)}^{2} d x and 鈭� \frac{2 - e^{x}}{e^{x}} d x$ .

Step by step solution

Step 1. Given Information

Find three integrals in Exercises 21鈥�70 that we can anti-differentiate immediately after algebraic simplification.

Step 2. The first integrals in Exercises 21–70 that we can anti-differentiate immediately after algebraic simplification.

$鈭� \frac{\sqrt{x} + 1}{x} d x$

After algebraic simplification

$鈭� \frac{\sqrt{x} + 1}{x} d x = 鈭� (\frac{\sqrt{x}}{x} + \frac{1}{x}) d x = 鈭� (\frac{1}{\sqrt{x}} + \frac{1}{x}) d x$

Now we can anti-differentiate immediately.

Step 3. The second integrals in Exercises 21–70 that we can anti differentiate immediately after algebraic simplification.

$鈭� x^{4} {(x^{3} + 1)}^{2} d x$

After algebraic simplification

$鈭� x^{4} {(x^{3} + 1)}^{2} d x = 鈭� x^{4} \{{(x^{3})}^{2} + 2 脳 1 脳 x^{3} + 1\} d x 鈭� x^{4} {(x^{3} + 1)}^{2} d x = 鈭� x^{4} \{x^{6} + 2 x^{3} + 1\} d x 鈭� x^{4} {(x^{3} + 1)}^{2} d x = 鈭� x^{4} x^{6} + 2 x^{3} x^{4} + 1 路 x^{4} d x 鈭� x^{4} {(x^{3} + 1)}^{2} d x = 鈭� x^{10} + 2 x^{7} + x^{4} d x$

Now we can anti-differentiate immediately.

Step 4. The third integrals in Exercises 21–70 that we can anti differentiate immediately after algebraic simplification.

$鈭� \frac{2 - e^{x}}{e^{x}} d x$

After algebraic simplification.

$鈭� \frac{2 - e^{x}}{e^{x}} d x = 鈭� (\frac{2}{e^{x}} - \frac{e^{x}}{e^{x}}) d x$

Now we can anti-differentiate immediately.

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91影视

Find three integrals in Exercises 21鈥�70 that we can anti-differentiate immediately after algebraic simplification.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The first integrals in Exercises 21–70 that we can anti-differentiate immediately after algebraic simplification.

Step 3. The second integrals in Exercises 21–70 that we can anti differentiate immediately after algebraic simplification.

Step 4. The third integrals in Exercises 21–70 that we can anti differentiate immediately after algebraic simplification.

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