What is the integral of (cos(x))/(1-cos^2(x)) ?

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

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integral of (cos(x))/(1-cos^2(x))

\int \frac{cos ( x )}{1 - cos ^{2} ( x )} d x

- csc (x) + C

Solution steps

\int \frac{cos ( x )}{1 - cos ^{2} ( x )} d x

Rewrite using trig identities

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

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{u}

= - \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

- y^{^{'''}} - y^{^{''}} + 5 y^{^{''}} - 3 = 0

\frac{\partial}{\partial x} (17 - 4 x^{2} - y^{2})

\frac{\partial}{\partial x} (\frac{y}{cos ( x )})

\frac{d}{d x} (\frac{4}{5} ln ((9 x^{2} - 6)^{7}))

\int_{2}^{4} \frac{( 2 x - 3 )}{6} d x

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