What is the integral of (csc^2(x))/(cot^5(x)) ?

The integral of (csc^2(x))/(cot^5(x)) is (tan^4(x))/4+C

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integral of (csc^2(x))/(cot^5(x))

\int \frac{csc ^{2} ( x )}{cot ^{5} ( x )} d x

\frac{tan ^{4} ( x )}{4} + C

Solution steps

\int \frac{csc ^{2} ( x )}{cot ^{5} ( x )} d x

Rewrite using trig identities

= \int (1 + tan^{2} (x)) tan^{3} (x) d x

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{u ^{4}}{4}

Substitute back

u = tan (x)

= \frac{tan ^{4} ( x )}{4}

Add a constant to the solution

= \frac{tan ^{4} ( x )}{4} + C

n = 1 \sum \infty \frac{1}{1 3 ^{n} - 5 ^{n}}

(1, - 5), (- 5, 5)

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

\int 6 e^{- 2 x} d x

\frac{d}{d x} ((1 - x)^{2} + 10 (y - x^{2})^{2})

What is the integral of (csc^2(x))/(cot^5(x)) ?
The integral of (csc^2(x))/(cot^5(x)) is (tan^4(x))/4+C