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

The integral of tan^2(x)csc(x) is sec(x)+C

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integral of tan^2(x)csc(x)

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

sec (x) + C

Solution steps

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

Simplify

tan^{2} (x) csc (x) : sec (x) tan (x)

= \int sec (x) tan (x) d x

Apply u-substitution

: \int 1 d u

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = sec (x)

= 1 \cdot sec (x)

Simplify

= sec (x)

Add a constant to the solution

= sec (x) + C

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What is the integral of tan^2(x)csc(x) ?
The integral of tan^2(x)csc(x) is sec(x)+C