Q. 30

Question

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.

$\int 5 \sin (2 x + 1) d x$

Step-by-Step Solution

Verified

Answer

The solution of the integral is $- \frac{5}{2} (\cos (2 x + 1)) + C .$

1Step 1. Given Information.

The given integral is $\int 5 \sin (2 x + 1) d x .$

2Step 2. Solve.

By solving the integral we get,

$\int 5 \sin (2 x + 1) d x = 5 \int \sin (2 x + 1) d x = 5 (- \frac{1}{2} \cos (2 x + 1)) + C = - \frac{5}{2} (\cos (2 x + 1)) + C$

3Step 3. Verification.

To verify the answer we differentiate it.

On differentiating we get,

$- \frac{5}{2} (\cos (2 x + 1)) + C = \frac{d}{d x} (- \frac{5}{2} \cos (2 x + 1)) + \frac{d}{d x} C = - 2 (- \frac{5}{2} \sin (2 x + 1)) + 0 = 5 \sin (2 x + 1)$

Hence proved.

Q. 29

Q. 31

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Q. 29

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Q. 31

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Q. 32

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