integral of ycos(y)sin^2(y)

解答

\int y cos (y) sin^{2} (y) d y

\frac{1}{3} y sin^{3} (y) - \frac{1}{3} (- cos (y) + \frac{cos ^{3} ( y )}{3}) + C

求解步骤

\int y cos (y) sin^{2} (y) d y

使用分布积分法

= \frac{1}{3} y sin^{3} (y) - \int \frac{1}{3} sin^{3} (y) d y

\int \frac{1}{3} sin^{3} (y) d y = \frac{1}{3} (- cos (y) + \frac{cos ^{3} ( y )}{3})

= \frac{1}{3} y sin^{3} (y) - \frac{1}{3} (- cos (y) + \frac{cos ^{3} ( y )}{3})

解答补常数

= \frac{1}{3} y sin^{3} (y) - \frac{1}{3} (- cos (y) + \frac{cos ^{3} ( y )}{3}) + C

t an g e n t \frac{1}{x}, at x = 2

a re a y = e^{x}, y = e^{3 x}, x = ln (2), x = ln (3)

d er i v a t i v e [x + (x + sin^{2} (x))^{5}]^{7}

d er i v a t i v e 6 (2 x^{3} + 3) 6 x^{2}

\int \frac{2 - 4 x ^{2}}{x - x ^{3}} d x