Changes

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Then, we cross multiply diagonally from the left to the right and we add the product to the product of the next product, alternating signs as we go (remember to start with a minus). So then the integral becomes:

Terms are multiplied diagonally from the left to the right and we add the product to the product of the next product, alternating signs with each step.

 

<math>(x^4)(-cos(x)) = -x^4cos(x)</math>

 

So then the integral becomes:

:<big><math>\int x^4 sin(x)\,dx</math></big> = <big><math>\ -x^4cos(x)-(-4x^3sin(x))+(12x^4cos(x))-(-24xsin(x))+(24cos(x))</math></big>=<big><math>\ -x^4cos(x)+4x^3sin(x)+12x^2cos(x)+24xsin(x)-24cos(x)+c</math></big>

:<big><math>\int x^4 sin(x)\,dx</math></big> = <big><math>\ -x^4cos(x)-(-4x^3sin(x))+(12x^4cos(x))-(-24xsin(x))+(24cos(x))</math></big>=<big><math>\ -x^4cos(x)+4x^3sin(x)+12x^2cos(x)+24xsin(x)-24cos(x)+c</math></big>