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

解

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

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

解答ステップ

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

部分積分を適用する

= [- \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}

簡素化

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

限度を計算する:

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

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