What is the integral of tan(x)sec^4(x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of tan(x)sec^4(x)

\int tan (x) sec^{4} (x) d x

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

Solution steps

\int tan (x) sec^{4} (x) d x

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

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

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

Substitute back

u = sec (x)

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

Add a constant to the solution

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

y^{^{''}} + 2 y^{^{'}} + 3 y = 0

y = x^{3} - 3 x^{2} - 27 x + 14, y = x + 14

\int \frac{x ^{3} + 6 x ^{2} + 3 x + 6}{x ^{3} + 2 x ^{2}} d x

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

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

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