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

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

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

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

- csc (x) + C

Solution steps

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

Apply u-substitution

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

Apply the Power Rule

= - \frac{1}{u}

Substitute back

u = sin (x)

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

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

= - csc (x)

Add a constant to the solution

= - csc (x) + C

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\frac{d y}{d x} + 2 x^{- 1} y = 6 x^{4} y^{2}

(\frac{1}{8}) y^{^{''}} + 4 y^{^{'}} + 20 y = 0

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