What is the integral of 3arctan(x) ?

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

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integral of 3arctan(x)

\int 3 arctan (x) d x

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

Solution steps

\int 3 arctan (x) d x

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

5 x^{2} + \frac{1}{x ^{2}}

\frac{x + 1}{x ^{3} + x - 3}

x \to 1 lim (x ln (x))

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

\frac{d}{d x} (2 - 5 x)

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