What is the integral of (sec(x)tan(x)+4x) ?

The integral of (sec(x)tan(x)+4x) is sec(x)+2x^2+C

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integral of (sec(x)tan(x)+4x)

\int (sec (x) tan (x) + 4 x) d x

sec (x) + 2 x^{2} + C

Solution steps

\int sec (x) tan (x) + 4 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 sec (x) tan (x) d x + \int 4 x d x

\int sec (x) tan (x) d x = sec (x)

\int 4 x d x = 2 x^{2}

= sec (x) + 2 x^{2}

Add a constant to the solution

= sec (x) + 2 x^{2} + C

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What is the integral of (sec(x)tan(x)+4x) ?
The integral of (sec(x)tan(x)+4x) is sec(x)+2x^2+C