What is the integral of ((tan(x))/(cot(x))+1) ?

The integral of ((tan(x))/(cot(x))+1) is tan(x)+C

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integral of ((tan(x))/(cot(x))+1)

\int (\frac{tan ( x )}{cot ( x )} + 1) d x

tan (x) + C

Solution steps

\int \frac{tan ( x )}{cot ( x )} + 1 d x

Simplify

\frac{tan ( x )}{cot ( x )} + 1 : 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))+1) ?
The integral of ((tan(x))/(cot(x))+1) is tan(x)+C