What is the integral of (-sec^2(x))/5 ?

The integral of (-sec^2(x))/5 is -1/5 tan(x)+C

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integral of (-sec^2(x))/5

\int \frac{- sec ^{2} ( x )}{5} d x

- \frac{1}{5} tan (x) + C

Solution steps

\int \frac{- sec ^{2} ( x )}{5} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{- 1}{5} \cdot \int sec^{2} (x) d x

Simplify

= (- \frac{1}{5}) \cdot \int sec^{2} (x) d x

Use the common integral:

\int sec^{2} (x) d x = tan (x)

= (- \frac{1}{5}) tan (x)

Simplify

= - \frac{1}{5} tan (x)

Add a constant to the solution

= - \frac{1}{5} tan (x) + C

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What is the integral of (-sec^2(x))/5 ?
The integral of (-sec^2(x))/5 is -1/5 tan(x)+C