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

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

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

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

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

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int cos (5 x) d x = \frac{1}{5} sin (5 x)

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

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

Add a constant to the solution

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

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