What is the integral of-3x^2cos(x) ?

The integral of-3x^2cos(x) is -3(x^2sin(x)-2(-xcos(x)+sin(x)))+C

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integral of-3x^2cos(x)

\int - 3 x^{2} cos (x) d x

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

Solution steps

\int - 3 x^{2} cos (x) d x

Take the constant out:

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

= - 3 \cdot \int x^{2} cos (x) d x

Apply Integration By Parts

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

= - 3 (x^{2} sin (x) - \int 2 x sin (x) d x)

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

= - 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))

Add a constant to the solution

= - 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))) + C

\int \frac{3 + 3 x - 2 x ^{2}}{5 - 7 x + 3 x ^{2} - x ^{3}} d x

\int \frac{8 x}{4 x ^{2} - 5} d x

\int (cos (x) - 1)^{2} d x

\int (sin (x))^{n} \cdot cos (x) d x

\int x^{3} \frac{1}{x + 1} d x

What is the integral of-3x^2cos(x) ?
The integral of-3x^2cos(x) is -3(x^2sin(x)-2(-xcos(x)+sin(x)))+C