What is the integral of 2arctan(3x) ?

The integral of 2arctan(3x) is 2(xarctan(3x)-1/6 ln|9x^2+1|)+C

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integral of 2arctan(3x)

\int 2 arctan (3 x) d x

2 (x arctan (3 x) - \frac{1}{6} ln 9 x^{2} + 1) + C

Solution steps

\int 2 arctan (3 x) d x

Take the constant out:

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

= 2 \cdot \int arctan (3 x) d x

Apply Integration By Parts

: x arctan (3 x) - \int \frac{3 x}{9 x ^{2} + 1} d x

= 2 (x arctan (3 x) - \int \frac{3 x}{9 x ^{2} + 1} d x)

\int \frac{3 x}{9 x ^{2} + 1} d x = \frac{1}{6} ln 9 x^{2} + 1

= 2 (x arctan (3 x) - \frac{1}{6} ln 9 x^{2} + 1)

Add a constant to the solution

= 2 (x arctan (3 x) - \frac{1}{6} ln 9 x^{2} + 1) + C

\int - x e^{- l n (x)} d x

f (x) = 2 x^{3} + 3 x^{2}, at x = 1

\int x^{2} f (x) d x

\int 4 e^{t} d t

\frac{d y}{d x} = 10 + 5 sin (\frac{x}{4}) - \frac{y}{100}

What is the integral of 2arctan(3x) ?
The integral of 2arctan(3x) is 2(xarctan(3x)-1/6 ln|9x^2+1|)+C