What is the integral of xsin^2(x)cos(x) ?

The integral of xsin^2(x)cos(x) is 1/3 xsin^3(x)-1/3 (-cos(x)+(cos^3(x))/3)+C

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integral of xsin^2(x)cos(x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\frac{\partial}{\partial y} (\frac{( x + y )}{y + z})

\int e^{- 4 θ} cos (2 θ) d θ

\int tan (X) d X

\frac{d y}{d x} = 4 y

y = \frac{6}{x}

What is the integral of xsin^2(x)cos(x) ?
The integral of xsin^2(x)cos(x) is 1/3 xsin^3(x)-1/3 (-cos(x)+(cos^3(x))/3)+C