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marissa [1.9K]
3 years ago
6

Use integration by parts to find the integrals in Exercise. ∫(4x-12)e-8x dx.

Mathematics
1 answer:
stepladder [879]3 years ago
5 0

Answer:

e(2x^{2} -12x)-4x^{2}+C

Step-by-step explanation:

We have been given an indefinite integral as \int \left(4x-12\right)e-8x\:dx. We are asked to find the given integral.

Let us solve our given problem.

\int \left(4x-12\right)e\:dx-\int 8x\:dx

Take out constant:

e\int \left(4x-12\right)\:dx-8\int x\:dx

e(\int 4x\:dx -\int 12\right\:dx)-8\int x\:dx

e(\frac{4x^{1+1}}{2} -12x)-8*\frac{x^{1+1}}{1+1}+C

e(\frac{4x^{2}}{2} -12x)-8*\frac{x^{2}}{2}+C

e(2x^{2} -12x)-4x^{2}+C

Therefore, our required integral would be e(2x^{2} -12x)-4x^{2}+C.

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