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Popular >

integral of sech(ax)

Solution

\int sech (a x) d x

Solution

\frac{1}{a} arctan (sinh (a x)) + C

Solution steps

\int sech (a x) d x

Apply u-substitution

: \int \frac{sech ( u )}{a} d u

= \int \frac{sech ( 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 sech (u) d u

Use the common integral:

\int sech (u) d u = arctan (sinh (u))

= \frac{1}{a} arctan (sinh (u))

Substitute back

u = a x

= \frac{1}{a} arctan (sinh (a x))

Add a constant to the solution

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

Popular Examples

integral of-(2cos(s))/(sin^2(s))

\int - \frac{2 cos ( s )}{sin ^{2} ( s )} d s

integral of (2x^2)/(x^2+9)

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

integral of (t+5)/(t^2+t-2)

\int \frac{t + 5}{t ^{2} + t - 2} d t

integral of (e^4-5^pi)

\int (e^{4} - 5^{π}) d x

integral of (3x^2-x)^2

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

Frequently Asked Questions (FAQ)

What is the integral of sech(ax) ?
The integral of sech(ax) is 1/a arctan(sinh(ax))+C