What is the integral from 1 to 4 of 2^xx ?

The integral from 1 to 4 of 2^xx is (62ln(2)-14)/(ln^2(2))

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integral from 1 to 4 of 2^xx

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

\frac{62 ln ( 2 ) - 14}{ln ^{2} ( 2 )}

Decimal

60.30792 \dots

Solution steps

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

Apply Integration By Parts

= [\frac{2 ^{x} x}{ln ( 2 )} - \int \frac{2 ^{x}}{ln ( 2 )} d x]_{1}^{4}

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

= [\frac{2 ^{x} x}{ln ( 2 )} - \frac{2 ^{x}}{ln ^{2} ( 2 )}]_{1}^{4}

Compute the boundaries:

\frac{62 ln ( 2 ) - 14}{ln ^{2} ( 2 )}

= \frac{62 ln ( 2 ) - 14}{ln ^{2} ( 2 )}

What is the integral from 1 to 4 of 2^xx ?
The integral from 1 to 4 of 2^xx is (62ln(2)-14)/(ln^2(2))