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

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

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integral of x^2(cos(x))

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int \frac{cos ( t )}{( 4 sin ( t ) + 12 ) ^{2}} d t

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\int cos (x) d (sin (x)) d x

\int x^{2} \cdot 5^{(x - 1)} d x

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