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

The integral of-x^2y^2sin(x) is -y^2(-x^2cos(x)+2(xsin(x)+cos(x)))+C

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integral of-x^2y^2sin(x)

\int - x^{2} y^{2} sin (x) d x

- y^{2} (- x^{2} cos (x) + 2 (x sin (x) + cos (x))) + C

Solution steps

\int - x^{2} y^{2} sin (x) d x

Take the constant out:

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

= - y^{2} \cdot \int sin (x) x^{2} d x

Apply Integration By Parts

: - x^{2} cos (x) - \int - 2 x cos (x) d x

= - y^{2} (- x^{2} cos (x) - \int - 2 x cos (x) d x)

\int - 2 x cos (x) d x = - 2 (x sin (x) + cos (x))

= - y^{2} (- x^{2} cos (x) - (- 2 (x sin (x) + cos (x))))

Simplify

= - y^{2} (- x^{2} cos (x) + 2 (x sin (x) + cos (x)))

Add a constant to the solution

= - y^{2} (- x^{2} cos (x) + 2 (x sin (x) + cos (x))) + C

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

\int \frac{x ^{2} - 7 x + 2}{x ^{2}} d x

\int \frac{4}{1 - 2 x} d x

\int \frac{x ^{3} + 2 x ^{2} + 5}{x} d x

\int \frac{1}{m} d m

What is the integral of-x^2y^2sin(x) ?
The integral of-x^2y^2sin(x) is -y^2(-x^2cos(x)+2(xsin(x)+cos(x)))+C