What is the integral of sqrt((argsinh(x))/(x^2+1)) ?

The integral of sqrt((argsinh(x))/(x^2+1)) is sqrt((sinh(x)ar)/(1+x^2)) 2/3 g^{3/2}+C

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integral of sqrt((argsinh(x))/(x^2+1))

\int \frac{a r g sinh ( x )}{x ^{2} + 1}

\frac{sinh ( x ) a r}{1 + x ^{2}} \frac{2}{3} g^{\frac{3}{2}} + C

Solution steps

\int \frac{a r g sinh ( x )}{x ^{2} + 1} d g

\frac{sinh ( x ) a r g}{1 + x ^{2}} = \frac{sinh ( x ) a r}{1 + x ^{2}} g

= \int \frac{sinh ( x ) a r}{1 + x ^{2}} g d g

Take the constant out:

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

= \frac{sinh ( x ) a r}{1 + x ^{2}} \cdot \int g d g

Apply the Power Rule

= \frac{sinh ( x ) a r}{1 + x ^{2}} \frac{2}{3} g^{\frac{3}{2}}

Add a constant to the solution

= \frac{sinh ( x ) a r}{1 + x ^{2}} \frac{2}{3} g^{\frac{3}{2}} + C

What is the integral of sqrt((argsinh(x))/(x^2+1)) ?
The integral of sqrt((argsinh(x))/(x^2+1)) is sqrt((sinh(x)ar)/(1+x^2)) 2/3 g^{3/2}+C