integral of (cos(7x)-xsin(4)x^2)

解

\int (cos (7 x) - x sin (4) x^{2}) d x

\frac{1}{7} sin (7 x) - \frac{1}{4} sin (4) x^{4} + C

解答ステップ

\int cos (7 x) - x sin (4) x^{2} 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 cos (7 x) d x - \int x sin (4) x^{2} d x

\int cos (7 x) d x = \frac{1}{7} sin (7 x)

\int x sin (4) x^{2} d x = \frac{1}{4} sin (4) x^{4}

= \frac{1}{7} sin (7 x) - \frac{1}{4} sin (4) x^{4}

定数を解答に追加する

= \frac{1}{7} sin (7 x) - \frac{1}{4} sin (4) x^{4} + C