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

The integral of (sin(x))/((cos(x))^5) is 1/4 sec^4(x)+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(x))^5)

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

\frac{1}{4} sec^{4} (x) + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{u ^{5}} d u

= \int - \frac{1}{u ^{5}} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{1}{u ^{5}} d u

Apply the Power Rule

: - \frac{1}{4 u ^{4}}

= - (- \frac{1}{4 u ^{4}})

Substitute back

u = cos (x)

= - (- \frac{1}{4 cos ^{4} ( x )})

Simplify

- (- \frac{1}{4 cos ^{4} ( x )}) : \frac{1}{4} sec^{4} (x)

= \frac{1}{4} sec^{4} (x)

Add a constant to the solution

= \frac{1}{4} sec^{4} (x) + C

3 x^{2}

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

\int (- 6 x^{3} + 9 x^{2} + 4 x - 3) d x

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

\int x 3 - 2 x d x

What is the integral of (sin(x))/((cos(x))^5) ?
The integral of (sin(x))/((cos(x))^5) is 1/4 sec^4(x)+C