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

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

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integral of x^4cos(x)

\int x^{4} cos (x) d x

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

Solution steps

\int x^{4} cos (x) d x

Apply Integration By Parts

: x^{4} sin (x) - \int 4 x^{3} sin (x) d x

= x^{4} sin (x) - \int 4 x^{3} sin (x) d x

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

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

Add a constant to the solution

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

\frac{5}{( 3 x ^{2} - x ) ^{4}}

\frac{d}{d x} (\frac{1}{x - a})

(1 - e^{- a x})^{2}

\frac{3 e ^{(- 2 s)}}{( s ^{2} - 4 s + 3 )}

ln (100 sin^{2} (x))

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