What is the integral from 1 to 2 of (2^x)/(x^2) ?

The integral from 1 to 2 of (2^x)/(x^2) is ln(2)\Ei(ln(2^2))-ln(2)\Ei(ln(2))

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integral from 1 to 2 of (2^x)/(x^2)

\int_{1}^{2} \frac{2 ^{x}}{x ^{2}} d x

ln (2) Ei (ln (2^{2})) - ln (2) Ei (ln (2))

Solution steps

\int_{1}^{2} \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]_{1}^{2}

= [- \frac{2 ^{x}}{x} - \int - \frac{ln ( 2 ) \cdot 2 ^{x}}{x} d x]_{1}^{2}

\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})))]_{1}^{2}

Simplify

= [- \frac{2 ^{x}}{x} + ln (2) Ei (ln (2^{x}))]_{1}^{2}

Compute the boundaries:

ln (2) Ei (ln (2^{2})) - ln (2) Ei (ln (2))

= ln (2) Ei (ln (2^{2})) - ln (2) Ei (ln (2))

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\int_{1}^{2} 4 x^{3} + 3 x^{2} + 4 x + 2 d x

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\int_{0}^{\frac{π}{2}} 2 cos^{4} (x) d x

\int_{- r}^{r} (r^{2} - x^{2}) d x

What is the integral from 1 to 2 of (2^x)/(x^2) ?
The integral from 1 to 2 of (2^x)/(x^2) is ln(2)\Ei(ln(2^2))-ln(2)\Ei(ln(2))