What is the integral of (sec^2(3sqrt(t)))/(sqrt(t)) ?

The integral of (sec^2(3sqrt(t)))/(sqrt(t)) is 2/3 tan(3sqrt(t))+C

Popular >

integral of (sec^2(3sqrt(t)))/(sqrt(t))

\int \frac{sec ^{2} ( 3 t )}{t} d t

\frac{2}{3} tan (3 t) + C

Solution steps

\int \frac{sec ^{2} ( 3 t )}{t} d t

Apply u-substitution

: \int \frac{2 sec ^{2} ( u )}{3} d u

= \int \frac{2 sec ^{2} ( u )}{3} d u

Take the constant out:

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

= \frac{2}{3} \cdot \int sec^{2} (u) d u

Use the common integral:

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

= \frac{2}{3} tan (u)

Substitute back

u = 3 t

= \frac{2}{3} tan (3 t)

Add a constant to the solution

= \frac{2}{3} tan (3 t) + C

\int \frac{( x + 2 )}{x ^{4} + 2 x ^{3} + x ^{2}} d x

\int 3 x^{2} e^{3 x} d x

\int x^{3} (5 + x^{4})^{7} d x

\int cos (\frac{x}{2}) cos (\frac{x}{3}) d x

\int \frac{e ^{x}}{x} (1 + x ln (x)) d x

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