What is the integral of arctan(sqrt(3x-1)) ?

The integral of arctan(sqrt(3x-1)) is xarctan(sqrt(3x-1))-1/3 sqrt(3x-1)+C

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integral of arctan(sqrt(3x-1))

\int arctan (3 x - 1) d x

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

Solution steps

\int arctan (3 x - 1) d x

Apply Integration By Parts

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

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

\int \frac{1}{2 3 x - 1} d x = \frac{1}{3} 3 x - 1

= x arctan (3 x - 1) - \frac{1}{3} 3 x - 1

Add a constant to the solution

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

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What is the integral of arctan(sqrt(3x-1)) ?
The integral of arctan(sqrt(3x-1)) is xarctan(sqrt(3x-1))-1/3 sqrt(3x-1)+C