What is the integral of ycos(y)sin^2(y) ?

The integral of ycos(y)sin^2(y) is 1/3 ysin^3(y)-1/3 (-cos(y)+(cos^3(y))/3)+C

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

\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

Solution steps

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

Apply Integration By Parts

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

= \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})

Add a constant to the solution

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

\frac{1}{x}, at x = 2

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

[x + (x + sin^{2} (x))^{5}]^{7}

6 (2 x^{3} + 3) 6 x^{2}

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

What is the integral of ycos(y)sin^2(y) ?
The integral of ycos(y)sin^2(y) is 1/3 ysin^3(y)-1/3 (-cos(y)+(cos^3(y))/3)+C