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

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

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

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

- cot (x) + C

Solution steps

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

Simplify

cot^{2} (x) (1 + tan^{2} (x)) : csc^{2} (x)

= \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

6 t^{4}

f (x) = 4 - x^{2}, at x = - 1

\int \frac{1}{10 x ^{7}} d x

y^{'} = y (3 - y)

\int (cos (y) sin (x)) d y

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