What is the integral of (1+cot^2(x)) ?

The integral of (1+cot^2(x)) is -cot(x)+C

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integral of (1+cot^2(x))

\int (1 + cot^{2} (x)) d x

- cot (x) + C

Solution steps

\int 1 + cot^{2} (x) d x

Rewrite using trig identities

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

Use the common integral:

\int csc^{2} (x) d x = - cot (x)

= - cot (x)

Add a constant to the solution

= - cot (x) + C

\int csc^{4} (3 x - 1) d x

\int - 3 x^{- 3} d x

\int \frac{1}{sin ( 2 y )} d y

\int \frac{sin ( 2 x )}{1 + ( cos ( x ) ) ^{2}} d x

\int \frac{6}{( 2 x + 3 x ^{2} )} d x

What is the integral of (1+cot^2(x)) ?
The integral of (1+cot^2(x)) is -cot(x)+C