What is the integral of (-cos(x))/(sin^4(x)) ?

The integral of (-cos(x))/(sin^4(x)) is 1/3 csc^3(x)+C

Popular >

integral of (-cos(x))/(sin^4(x))

\int \frac{- cos ( x )}{sin ^{4} ( x )} d x

\frac{1}{3} csc^{3} (x) + C

Solution steps

\int \frac{- cos ( x )}{sin ^{4} ( 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 ^{4} ( x )} d x

Apply u-substitution

: \int \frac{1}{u ^{4}} d u

= - \int \frac{1}{u ^{4}} d u

Apply the Power Rule

: - \frac{1}{3 u ^{3}}

= - (- \frac{1}{3 u ^{3}})

Substitute back

u = sin (x)

= - (- \frac{1}{3 sin ^{3} ( x )})

Simplify

- (- \frac{1}{3 sin ^{3} ( x )}) : \frac{1}{3} csc^{3} (x)

= \frac{1}{3} csc^{3} (x)

Add a constant to the solution

= \frac{1}{3} csc^{3} (x) + C

\int \frac{4 ^{l n (x)}}{x} d x

\int \frac{csc ( 5 + ln ( t ) ) cot ( 5 + ln ( t ) )}{t} d t

\int (x + 3) (x + 7) d x

\int ln (x) (10 x^{3} + 14 x + 3) d x

\int \frac{6 x ^{3} - 7 x + 5}{x ^{3} - x ^{2}} d x

What is the integral of (-cos(x))/(sin^4(x)) ?
The integral of (-cos(x))/(sin^4(x)) is 1/3 csc^3(x)+C