What is the integral of (sec(x)tan(x))^2 ?

The integral of (sec(x)tan(x))^2 is (tan^3(x))/3+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sec(x)tan(x))^2

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

\frac{tan ^{3} ( x )}{3} + C

Solution steps

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

Rewrite using trig identities

= \int (1 + tan^{2} (x)) tan^{2} (x) d x

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = tan (x)

= \frac{tan ^{3} ( x )}{3}

Add a constant to the solution

= \frac{tan ^{3} ( x )}{3} + C

\int \frac{tan ^{3} ( θ ) + 1}{cos ^{2} ( θ )} d θ

\int (e^{7 x} + 8) (e^{- 4 x} + 21) d x

\int \frac{7}{( x - 2 ) ( x + 5 )} d x

\int \frac{9 x ^{2}}{x ^{3} + 1} d x

\int \frac{2 x}{4} d x

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