What is the integral of tan^3(x)*sec^2(x) ?

The integral of tan^3(x)*sec^2(x) is (tan^4(x))/4+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of tan^3(x)*sec^2(x)

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

\frac{tan ^{4} ( x )}{4} + C

Solution steps

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

Rewrite using trig identities

= \int (1 + tan^{2} (x)) tan^{3} (x) d x

Apply u-substitution

= \int u^{3} d u

Apply the Power Rule

= \frac{u ^{4}}{4}

Substitute back

u = tan (x)

= \frac{tan ^{4} ( x )}{4}

Add a constant to the solution

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

What is the integral of tan^3(x)*sec^2(x) ?
The integral of tan^3(x)*sec^2(x) is (tan^4(x))/4+C