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

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

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integral of csc^2(x+1)

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

- cot (x + 1) + C

Solution steps

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

Rewrite using trig identities

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

Apply u-substitution

: \int csc^{2} (u) d u

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

Use the common integral:

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

= - cot (u)

Substitute back

u = x + 1

= - cot (x + 1)

Add a constant to the solution

= - cot (x + 1) + C

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