What is the integral of (sin(2x))/(1+3sin^2(x)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sin(2x))/(1+3sin^2(x))

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

\frac{1}{3} ln 1 + 3 sin^{2} (x) + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{3 u} d u

= \int \frac{1}{3 u} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} ln ∣ u ∣

Substitute back

u = 1 + 3 sin^{2} (x)

= \frac{1}{3} ln 1 + 3 sin^{2} (x)

Add a constant to the solution

= \frac{1}{3} ln 1 + 3 sin^{2} (x) + C

y^{^{'}} = sin (x + y)

\frac{d}{d t} (e^{9 t s i n (2 t)})

y^{^{''}} + 4 y^{^{'}} = t^{2} + 3 e^{t}

\int e^{- v} cos (w v) d v

\int 4 + x^{2} d x

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