What is the integral of (sin^3(x))/(cos^5(x)) ?

The integral of (sin^3(x))/(cos^5(x)) is (tan^4(x))/4+C

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integral of (sin^3(x))/(cos^5(x))

\int \frac{sin ^{3} ( x )}{cos ^{5} ( x )} d x

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

Solution steps

\int \frac{sin ^{3} ( x )}{cos ^{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

\frac{\partial}{\partial y} (e^{3 x - y^{2}})

\frac{d ^{2}}{d x ^{2}} (\frac{x}{e ^{x}})

\frac{d}{d x} (arccos (e^{5 x}))

\int_{- 3}^{3} (16 - x^{2}) - (x^{2} - 2) d x

What is the integral of (sin^3(x))/(cos^5(x)) ?
The integral of (sin^3(x))/(cos^5(x)) is (tan^4(x))/4+C