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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

integral

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

Apply the Power Rule

= \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

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