integral of (e^{4x}+3x^{1/4})

解

\int (e^{4 x} + 3 x^{\frac{1}{4}}) d x

\frac{1}{4} e^{4 x} + \frac{12}{5} x^{\frac{5}{4}} + C

解答ステップ

\int e^{4 x} + 3 x^{\frac{1}{4}} 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 e^{4 x} d x + \int 3 x^{\frac{1}{4}} d x

\int e^{4 x} d x = \frac{1}{4} e^{4 x}

\int 3 x^{\frac{1}{4}} d x = \frac{12}{5} x^{\frac{5}{4}}

= \frac{1}{4} e^{4 x} + \frac{12}{5} x^{\frac{5}{4}}

定数を解答に追加する

= \frac{1}{4} e^{4 x} + \frac{12}{5} x^{\frac{5}{4}} + C