integral of (((7-2x))/(x^{1/2)}+3(5-e^x+2e^3))

解

\int (\frac{( 7 - 2 x )}{x ^{\frac{1}{2}}} + 3 (5 - e^{x} + 2 e^{3})) d x

14 x^{\frac{1}{2}} - \frac{4}{3} x^{\frac{3}{2}} + 3 (5 x - e^{x} + 2 e^{3} x) + C

解答ステップ

\int \frac{7 - 2 x}{x ^{\frac{1}{2}}} + 3 (5 - e^{x} + 2 e^{3}) d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{7 - 2 x}{x ^{\frac{1}{2}}} d x + \int 3 (5 - e^{x} + 2 e^{3}) d x

\int \frac{7 - 2 x}{x ^{\frac{1}{2}}} d x = 14 x^{\frac{1}{2}} - \frac{4}{3} x^{\frac{3}{2}}

\int 3 (5 - e^{x} + 2 e^{3}) d x = 3 (5 x - e^{x} + 2 e^{3} x)

= 14 x^{\frac{1}{2}} - \frac{4}{3} x^{\frac{3}{2}} + 3 (5 x - e^{x} + 2 e^{3} x)

定数を解答に追加する

= 14 x^{\frac{1}{2}} - \frac{4}{3} x^{\frac{3}{2}} + 3 (5 x - e^{x} + 2 e^{3} x) + C