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

\frac{d}{d x} (6 x^{2} e^{- x})

y^{^{''}} + 4 y = 2 e^{x} + sin (2 x)

\frac{\partial}{\partial y} (\frac{x ^{2} + y ^{2}}{x ^{2} - y ^{2}})

\frac{\partial}{\partial x} (4 - x^{2} - 4 Y (x) (x)^{2})

\frac{d}{d x} (- x^{3} + 5 x^{2} - 6 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