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

The integral of 1/((sin(x)cot^2(x))) is sec(x)+C

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integral of 1/((sin(x)cot^2(x)))

integral

\frac{1}{( sin ( x ) cot ^{2} ( x ) )}

sec (x) + C

Solution steps

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

Simplify

\frac{1}{sin ( x ) cot ^{2} ( x )} : sec (x) tan (x)

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

Apply u-substitution

= \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

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