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

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

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integral of x^4sin(x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int \frac{y}{2} d y

f (x) = 5 x 2

[1]

\int 17 (tan (x)) (ln (cos (x))) d x

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