integral from 1 to 4 of 2^xx

解

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

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

十進法表記

60.30792 \dots

解答ステップ

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

部分積分を適用する

= [\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}

限度を計算する:

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

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