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

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

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

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

Solution steps

\int tan^{2} (x) sec^{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{50}{x ^{3}} d x

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

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

\int \frac{( t - t ^{2} ) ^{2}}{t t} d t

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

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