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

Popular >

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

\int sin (\frac{x}{4}) cos (\frac{3 x}{4}) d x

\int \frac{2 x - 1}{( x + 8 ) ( x - 9 )} d x

\int \frac{ln ( x + 3 )}{x + 3} d x

\int \frac{2 x ^{2} + x + 6}{x ^{2} + x - 2} d x

\int \frac{1}{( x + 1 ) ^{3} x ^{2} + 2 x - 3} d x

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