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Expert-verified Found in: Page 362 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # 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. $\int \left({x}^{2}-3{x}^{5}-7\right)dx$

The answer is $\frac{1}{3}{x}^{3}-\left(\frac{1}{2}\right){x}^{6}-7x+C.$

See the step by step solution

## Step 1. Given information.

The given integral is $\int \left({x}^{2}-3{x}^{5}-7\right)dx.$

## Step 2. Integration.

On integrating,

$\int \left({x}^{2}-3{x}^{5}-7\right)dx\phantom{\rule{0ex}{0ex}}=\int {x}^{2}dx-\int 3{x}^{5}dx-\int 7dx\phantom{\rule{0ex}{0ex}}=\frac{1}{3}{x}^{3}-3\left(\frac{1}{6}\right){x}^{6}-7x+C\phantom{\rule{0ex}{0ex}}=\frac{1}{3}{x}^{3}-\left(\frac{1}{2}\right){x}^{6}-7x+C$

## Step 3. Verification.

On Differentiating$\frac{1}{3}{x}^{3}-\left(\frac{1}{2}\right){x}^{6}-7x+C$, we get,

$\frac{1}{3}×3{x}^{2}-\frac{1}{2}×6{x}^{5}-7\phantom{\rule{0ex}{0ex}}={x}^{2}-3{x}^{5}-7$

Hence proved. ### Want to see more solutions like these? 