What is the integral of (-cos(x))/(sin^3(x)) ?

The integral of (-cos(x))/(sin^3(x)) is 1/2 csc^2(x)+C

Popular >

integral of (-cos(x))/(sin^3(x))

\int \frac{- cos ( x )}{sin ^{3} ( x )} d x

\frac{1}{2} csc^{2} (x) + C

Solution steps

\int \frac{- cos ( x )}{sin ^{3} ( x )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{cos ( x )}{sin ^{3} ( x )} d x

Rewrite using trig identities

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

Apply u-substitution

: \int - \frac{1}{2} d u

= - \int - \frac{1}{2} d u

Integral of a constant:

\int a d x = a x

= - (- \frac{1}{2}) u

Substitute back

u = csc^{2} (x)

= - (- \frac{1}{2}) csc^{2} (x)

Simplify

= \frac{1}{2} csc^{2} (x)

Add a constant to the solution

= \frac{1}{2} csc^{2} (x) + C

\int \frac{e ^{x^{2}}}{x ^{3}} d x

\int w ln (w - 2) d w

\int \frac{2 x - 1}{x ^{2} + x} d x

\int \frac{x}{1 - 4 x - x ^{2}} d x

\int \frac{x + 1}{x ^{2} + 4 x + 8} d x

What is the integral of (-cos(x))/(sin^3(x)) ?
The integral of (-cos(x))/(sin^3(x)) is 1/2 csc^2(x)+C