integral of xycos(y)

解答

\int x y cos (y) d y

x (y sin (y) + cos (y)) + C

求解步骤

\int x y cos (y) d y

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= x \cdot \int cos (y) y d y

使用分布积分法

= x (y sin (y) - \int sin (y) d y)

\int sin (y) d y = - cos (y)

= x (y sin (y) - (- cos (y)))

化简

= x (y sin (y) + cos (y))

解答补常数

= x (y sin (y) + cos (y)) + C

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

\int e^{7 x} \cdot sin (2 x) d x

\int \frac{18 x}{x ^{2} + 1} d x

\int (- \frac{A R x ^{2}}{2} + C) d x

\int \frac{1}{( 9 x ^{2} - 16 ) ^{3}} d x