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Popular >

integral of x^3*cos(x)

Solution

\int x^{3} \cdot cos (x) d x

Solution

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

Solution steps

\int x^{3} cos (x) d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

Popular Examples

xln(x)=y(1+sqrt(8+y^2))y^'(x),y(1)=1

x ln (x) = y (1 + 8 + y^{2}) y^{^{'}} (x), y (1) = 1

derivative of in(x^2+1)

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

(dy)/(dx)=y^2+1

\frac{d y}{d x} = y^{2} + 1

derivative of e^{(-x^2/8})

\frac{d}{d x} (e^{\frac{- x ^{2}}{8}})

integral of (ln(x))^4 1/x

\int (ln (x))^{4} \frac{1}{x} d x

Frequently Asked Questions (FAQ)

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