What is the integral of (4x^2+3x)cos(x) ?

The integral of (4x^2+3x)cos(x) is 4(x^2sin(x)-2(-xcos(x)+sin(x)))+3(xsin(x)+cos(x))+C

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integral of (4x^2+3x)cos(x)

\int (4 x^{2} + 3 x) cos (x) d x

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

Solution steps

\int (4 x^{2} + 3 x) cos (x) d x

Expand

(4 x^{2} + 3 x) cos (x) : 4 x^{2} cos (x) + 3 x cos (x)

= \int 4 x^{2} cos (x) + 3 x cos (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 x^{2} cos (x) d x + \int 3 x cos (x) d x

\int 4 x^{2} cos (x) d x = 4 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))

\int 3 x cos (x) d x = 3 (x sin (x) + cos (x))

= 4 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))) + 3 (x sin (x) + cos (x))

Add a constant to the solution

= 4 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))) + 3 (x sin (x) + cos (x)) + C

\frac{d}{d x} (x e^{3 x^{2} + 1})

\int (y^{2} - \frac{1}{y ^{2}})^{3} d y

\int cos (a t) d t

\int_{0}^{1} y e^{y} d y

x \to 0 lim (\frac{( x + 3 ) ^{2} - 9}{x})

What is the integral of (4x^2+3x)cos(x) ?
The integral of (4x^2+3x)cos(x) is 4(x^2sin(x)-2(-xcos(x)+sin(x)))+3(xsin(x)+cos(x))+C