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

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

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

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

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

Solution steps

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

Rewrite using trig identities

= \int tan (x) sec^{4} (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 = sec (x)

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

Add a constant to the solution

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

\frac{d}{d x} (5 x^{2} - 1)

\frac{d N}{d t} + N = Nt e^{(t + 2)}

n = 1 \sum \infty \frac{n !}{2 n - 1}

y^{^{'}} = \frac{5}{y + 2}

\frac{d}{d x} ((5 x^{6} + 8 x^{3})^{4})

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