What is the integral of sec^2(ax) ?

The integral of sec^2(ax) is 1/a tan(ax)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sec^2(ax)

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

\frac{1}{a} tan (a x) + C

Solution steps

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

Apply u-substitution

: \int \frac{sec ^{2} ( u )}{a} d u

= \int \frac{sec ^{2} ( u )}{a} d u

Take the constant out:

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

= \frac{1}{a} \cdot \int sec^{2} (u) d u

Use the common integral:

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

= \frac{1}{a} tan (u)

Substitute back

u = a x

= \frac{1}{a} tan (a x)

Add a constant to the solution

= \frac{1}{a} tan (a x) + C

\int + x^{3} ln (5 x) d x

\int \frac{1}{1000} e^{- \frac{x}{1000}} d x

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

\int (x^{2} - 1)^{3} d x

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