integral of x-2+3/((3x-5)^6)

解

\int x - 2 + \frac{3}{( 3 x - 5 ) ^{6}} d x

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

解答ステップ

\int x - 2 + \frac{3}{( 3 x - 5 ) ^{6}} 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 x d x - \int 2 d x + \int \frac{3}{( 3 x - 5 ) ^{6}} d x

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

\int 2 d x = 2 x

\int \frac{3}{( 3 x - 5 ) ^{6}} d x = - \frac{1}{5 ( 3 x - 5 ) ^{5}}

= \frac{x ^{2}}{2} - 2 x - \frac{1}{5 ( 3 x - 5 ) ^{5}}

定数を解答に追加する

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