What is the integral from ln(5/6) to infinity of (e^x)/(36e^{2x)+25} ?

The integral from ln(5/6) to infinity of (e^x)/(36e^{2x)+25} is pi/(120)

integral from ln(5/6) to infinity of (e^x)/(36e^{2x)+25}

\int_{l n (\frac{5}{6})}^{\infty} \frac{e ^{x}}{36 e ^{2 x} + 25} d x

\frac{π}{120}

Decimal

0.02617 \dots

Solution steps

\int_{l n (\frac{5}{6})}^{\infty} \frac{e ^{x}}{36 e ^{2 x} + 25} d x

Compute the indefinite integral:

\int \frac{e ^{x}}{36 e ^{2 x} + 25} d x = \frac{1}{30} arctan (\frac{6}{5} e^{x}) + C

Compute the boundaries:

\int_{l n (\frac{5}{6})}^{\infty} \frac{e ^{x}}{36 e ^{2 x} + 25} d x = \frac{π}{60} - \frac{π}{120}

= \frac{π}{60} - \frac{π}{120}

Simplify

= \frac{π}{120}

\frac{d y}{d x} + \frac{3}{x} y = \frac{ln ( x )}{x ^{2}}

\int - \frac{1}{x ^{2} - 1} d x

y^{^{'}} = sec^{2} (x) (2 + y)^{2}, y (π) = - 5

\frac{d}{d x} (8 4 x)

y^{^{''}} + 4 y = 3 sin (2 x)

What is the integral from ln(5/6) to infinity of (e^x)/(36e^{2x)+25} ?
The integral from ln(5/6) to infinity of (e^x)/(36e^{2x)+25} is pi/(120)