What is the integral of tan(x)(cot(x)+tan(x)) ?

The integral of tan(x)(cot(x)+tan(x)) is tan(x)+C

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integral of tan(x)(cot(x)+tan(x))

\int tan (x) (cot (x) + tan (x)) d x

tan (x) + C

Solution steps

\int tan (x) (cot (x) + tan (x)) d x

Simplify

tan (x) (cot (x) + tan (x)) : sec^{2} (x)

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

Use the common integral:

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

= tan (x)

Add a constant to the solution

= tan (x) + C

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What is the integral of tan(x)(cot(x)+tan(x)) ?
The integral of tan(x)(cot(x)+tan(x)) is tan(x)+C