What is the integral of 5x^2cos(x) ?

The integral of 5x^2cos(x) is 5(x^2sin(x)-2(-xcos(x)+sin(x)))+C

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integral of 5x^2cos(x)

\int 5 x^{2} cos (x) d x

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

Solution steps

\int 5 x^{2} cos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int x^{2} cos (x) d x

Apply Integration By Parts

= 5 (x^{2} sin (x) - \int 2 x sin (x) d x)

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

= 5 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))

Add a constant to the solution

= 5 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))) + C

\int (x - ln (x)) d x

in v erse l a pl a ce \frac{s + 2}{s ^{2} + 4 s + 13}

\int 5 sin^{5} (x) cos^{- \frac{3}{2}} (x) d x

\int cos^{3} (6 x) sin^{- 2} (6 x) d x

t an g e n t - x^{3} - 5 x^{2} + 3 x - 1

What is the integral of 5x^2cos(x) ?
The integral of 5x^2cos(x) is 5(x^2sin(x)-2(-xcos(x)+sin(x)))+C