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

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}

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