What is the integral of (2^x)/(x^2) ?

The integral of (2^x)/(x^2) is -(2^x)/x+ln(2)\Ei(ln(2^x))+C

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integral of (2^x)/(x^2)

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

- \frac{2 ^{x}}{x} + ln (2) Ei (ln (2^{x})) + C

Solution steps

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

Apply Integration By Parts

= - \frac{2 ^{x}}{x} - \int - \frac{ln ( 2 ) \cdot 2 ^{x}}{x} d x

\int - \frac{ln ( 2 ) \cdot 2 ^{x}}{x} d x = - ln (2) Ei (ln (2^{x}))

= - \frac{2 ^{x}}{x} - (- ln (2) Ei (ln (2^{x})))

Simplify

= - \frac{2 ^{x}}{x} + ln (2) Ei (ln (2^{x}))

Add a constant to the solution

= - \frac{2 ^{x}}{x} + ln (2) Ei (ln (2^{x})) + C

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What is the integral of (2^x)/(x^2) ?
The integral of (2^x)/(x^2) is -(2^x)/x+ln(2)\Ei(ln(2^x))+C