What is the integral of (cos^4(x))/(sin^2(x)) ?

The integral of (cos^4(x))/(sin^2(x)) is -cos^4(x)cot(x)-4(cos^3(x)sin(x)+3/8 (x-1/4 sin(4x)))+C

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integral of (cos^4(x))/(sin^2(x))

\int \frac{cos ^{4} ( x )}{sin ^{2} ( x )} d x

- cos^{4} (x) cot (x) - 4 (cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x))) + C

Solution steps

\int \frac{cos ^{4} ( x )}{sin ^{2} ( x )} d x

Apply Integration By Parts

: - cos^{4} (x) cot (x) - \int 4 cos^{3} (x) sin (x) cot (x) d x

= - cos^{4} (x) cot (x) - \int 4 cos^{3} (x) sin (x) cot (x) d x

\int 4 cos^{3} (x) sin (x) cot (x) d x = 4 (cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x)))

= - cos^{4} (x) cot (x) - 4 (cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x)))

Add a constant to the solution

= - cos^{4} (x) cot (x) - 4 (cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x))) + C

\frac{( s ^{2} )}{s ^{3} - 1}

\frac{\partial}{\partial x} (e^{- (x^{2} + y^{2})})

x \to 8 lim (x - 2)

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

x \to 2 lim (\frac{7}{( x - 2 ) ^{2}})

What is the integral of (cos^4(x))/(sin^2(x)) ?
The integral of (cos^4(x))/(sin^2(x)) is -cos^4(x)cot(x)-4(cos^3(x)sin(x)+3/8 (x-1/4 sin(4x)))+C