integral of (2e^x+sec(x)tan(x)-sqrt(x))

解

\int (2 e^{x} + sec (x) tan (x) - x) d x

2 e^{x} + sec (x) - \frac{2}{3} x^{\frac{3}{2}} + C

解答ステップ

\int 2 e^{x} + sec (x) tan (x) - x 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 2 e^{x} d x + \int sec (x) tan (x) d x - \int x d x

\int 2 e^{x} d x = 2 e^{x}

\int sec (x) tan (x) d x = sec (x)

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

= 2 e^{x} + sec (x) - \frac{2}{3} x^{\frac{3}{2}}

定数を解答に追加する

= 2 e^{x} + sec (x) - \frac{2}{3} x^{\frac{3}{2}} + C