Find the integral of \(8x e^{8x}\).

Integration by parts Integral(udv)=uv-integral(duv) In this case we will make u=x and dv=8e^(8x) so du=1 and v=e^(8x) Now integral(8xe^(8x)) => xe^(8x) - integral(e^(8x)) => xe^(8x) - e^(8x)/8 => (e^(8x))(x-1/8) Final answer: (E^(8x))(x-1/8) + some constant C Hope I helped :)

Answered by FirstSineOfMadness | 2024-06-10

To integrate 8 x e 8 x , we employ integration by parts. We let u = 8 x and d v = e 8 x d x , leading to the result ∫ 8 x e 8 x d x = e 8 x ( x − 8 1 ​ ) + C . This gives us a clear and complete solution to the integral.
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Answered by FirstSineOfMadness | 2024-12-26