What is the integral of (arctan(sqrt(x)))/(sqrt(x)) ?

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

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integral of (arctan(sqrt(x)))/(sqrt(x))

\int \frac{arctan ( x )}{x} d x

2 x arctan (x) - ln ∣ x + 1 ∣ + C

Solution steps

\int \frac{arctan ( x )}{x} d x

Apply Integration By Parts

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

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

\int \frac{1}{x + 1} d x = ln ∣ x + 1 ∣

= 2 x arctan (x) - ln ∣ x + 1 ∣

Add a constant to the solution

= 2 x arctan (x) - ln ∣ x + 1 ∣ + C

f (x) = tan^{4} (x^{3})

x \to 0 lim (\frac{5}{x ^{2}})

ln (3 x^{3} + 6 x^{2} + 2 x + 6)

x y^{2} y^{^{'}} = x + 9

\int x^{n} a x^{n + 1} + b d x

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