What is the integral of (5cos(x))/(sin^2(x)) ?

The integral of (5cos(x))/(sin^2(x)) is -5csc(x)+C

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integral of (5cos(x))/(sin^2(x))

\int \frac{5 cos ( x )}{sin ^{2} ( x )} d x

- 5 csc (x) + C

Solution steps

\int \frac{5 cos ( x )}{sin ^{2} ( x )} d x

Take the constant out:

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

= 5 \cdot \int \frac{cos ( x )}{sin ^{2} ( x )} d x

Apply u-substitution

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

= 5 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 5 (- \frac{1}{u})

Substitute back

u = sin (x)

= 5 (- \frac{1}{sin ( x )})

Simplify

5 (- \frac{1}{sin ( x )}) : - 5 csc (x)

= - 5 csc (x)

Add a constant to the solution

= - 5 csc (x) + C

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

\int \frac{x ^{2} + 4 x - 5}{x ^{3}} d x

\int \frac{1}{x ( 2 ln ( x ) + 1 )} d x

\int \frac{2}{3 x - 1} d x

\int x^{\frac{- 3}{4}} d x

What is the integral of (5cos(x))/(sin^2(x)) ?
The integral of (5cos(x))/(sin^2(x)) is -5csc(x)+C