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

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

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integral of 3x^2*cos(x)

\int 3 x^{2} \cdot 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 (3 x^{2} + 2 x^{2}) d x

\int \frac{3 ^{2 y} - 2 7 ^{y}}{9 ^{2 y}} d y

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

\int 2 ln (3 x + 1) d x

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