integral of (3x^2-4*5^x)

解

\int (3 x^{2} - 4 \cdot 5^{x}) d x

x^{3} - \frac{4 \cdot 5 ^{x}}{ln ( 5 )} + C

解答ステップ

\int 3 x^{2} - 4 \cdot 5^{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 3 x^{2} d x - \int 4 \cdot 5^{x} d x

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

\int 4 \cdot 5^{x} d x = \frac{4 \cdot 5 ^{x}}{ln ( 5 )}

= x^{3} - \frac{4 \cdot 5 ^{x}}{ln ( 5 )}

定数を解答に追加する

= x^{3} - \frac{4 \cdot 5 ^{x}}{ln ( 5 )} + C