What is the integral of 5arctan(x) ?

The integral of 5arctan(x) is 5(xarctan(x)-1/2 ln|x^2+1|)+C

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integral of 5arctan(x)

\int 5 arctan (x) d x

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

Solution steps

\int 5 arctan (x) d x

Take the constant out:

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

= 5 \cdot \int arctan (x) d x

Apply Integration By Parts

= 5 (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

= 5 (x arctan (x) - \frac{1}{2} ln x^{2} + 1)

Add a constant to the solution

= 5 (x arctan (x) - \frac{1}{2} ln x^{2} + 1) + C

What is the integral of 5arctan(x) ?
The integral of 5arctan(x) is 5(xarctan(x)-1/2 ln|x^2+1|)+C