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

The integral of (-sin(x))/(cos^3(x)) is -(tan^2(x))/2+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^3(x))

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

- \frac{tan ^{2} ( x )}{2} + C

Solution steps

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

Take the constant out:

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

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

Rewrite using trig identities

= - \int tan (x) sec^{2} (x) d x

Apply u-substitution

: \int u d u

= - \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= - \frac{u ^{2}}{2}

Substitute back

u = tan (x)

= - \frac{tan ^{2} ( x )}{2}

Add a constant to the solution

= - \frac{tan ^{2} ( x )}{2} + C

\int 4 x - 2 d x

\int sec (4 x) - cot (4 x) d x

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

\int (x^{2} - 1)^{4} (2 x) d x

\int \frac{1}{( x + 7 ) ^{5}} d x

What is the integral of (-sin(x))/(cos^3(x)) ?
The integral of (-sin(x))/(cos^3(x)) is -(tan^2(x))/2+C