What is the integral from 1 to infinity of 1/(sqrt(x)+x\sqrt{x)} ?

The integral from 1 to infinity of 1/(sqrt(x)+x\sqrt{x)} is pi-pi/2

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integral from 1 to infinity of 1/(sqrt(x)+x\sqrt{x)}

\int_{1}^{\infty} \frac{1}{x + x x} d x

π - \frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

\int_{1}^{\infty} \frac{1}{x + x x} d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{1}^{\infty} \frac{1}{x + x x} d x = π - \frac{π}{2}

= π - \frac{π}{2}

ln (\frac{e ^{x} + 1}{e ^{x} - 1})

\int_{1}^{2} \frac{1}{( 3 - 5 x ) ^{2}} d x

π^{x^{2}}

\int \frac{1}{5 - 4 x} d x

\frac{\partial}{\partial b} (\frac{a}{b})

What is the integral from 1 to infinity of 1/(sqrt(x)+x\sqrt{x)} ?
The integral from 1 to infinity of 1/(sqrt(x)+x\sqrt{x)} is pi-pi/2