integral from 4 to 8 of (2x+15)e^{0.25x}

解

\int_{4}^{8} (2 x + 15) e^{0.25 x} d x

516.69625 \dots

解答ステップ

\int_{4}^{8} (2 x + 15) e^{0.25 x} d x

2 x + 15

の共役で乗じる

\frac{4 x ^{2} - 225}{2 x - 15}

= \int_{4}^{8} \frac{4 x ^{2} - 225}{2 x - 15} e^{0.25 x} d x

未定義の (特異) 点を求める:

x = \frac{15}{2}

存在する場合は

b, a < b < c, f (b) =

未定義

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{4}^{\frac{15}{2}} \frac{4 x ^{2} - 225}{2 x - 15} e^{0.25 x} d x + \int_{\frac{15}{2}}^{8} \frac{4 x ^{2} - 225}{2 x - 15} e^{0.25 x} d x

\int_{4}^{\frac{15}{2}} \frac{4 x ^{2} - 225}{2 x - 15} e^{0.25 x} d x = 410.73517 \dots

\int_{\frac{15}{2}}^{8} \frac{4 x ^{2} - 225}{2 x - 15} e^{0.25 x} d x = 105.96107 \dots

= 410.73517 \dots + 105.96107 \dots

簡素化

= 516.69625 \dots