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

The integral of (sec^2(x))/(3+2tan(x)) is 1/2 ln|3+2tan(x)|+C

Popular >

integral of (sec^2(x))/(3+2tan(x))

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

\frac{1}{2} ln ∣ 3 + 2 tan (x) ∣ + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = 3 + 2 tan (x)

= \frac{1}{2} ln ∣ 3 + 2 tan (x) ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ 3 + 2 tan (x) ∣ + C

\int 2 1 + x^{2} d x

\int cos^{19} (x) sin (x) d x

\int (4 x^{\frac{2}{3}} - 4 x^{\frac{1}{5}}) d x

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

\int (2 + x + y e^{y}) d y

What is the integral of (sec^2(x))/(3+2tan(x)) ?
The integral of (sec^2(x))/(3+2tan(x)) is 1/2 ln|3+2tan(x)|+C