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romanna [79]
3 years ago
6

Use integration by parts to find the integrals in Exercise. ∫(x+6)ex dx.

Mathematics
1 answer:
skelet666 [1.2K]3 years ago
5 0

Answer:

xe^x+5e^x

Step-by-step explanation:

We have given integral \int (x+6)e^xdx

\int (xe^x+6e^x)dx

\int (I_1+I_2)dx , here I_1=xe^x and I_2=6e^x

Now first integrate I_1

So I_1=\int xe^x

Integrating by part

I_1=x\int e^x-\int e^x\frac{d}{dx}x

I_1=x e^x- e^x

I_2=6\int e^x=6e^x

So I=I_1+I_2=xe^x-e^x+6e^x=xe^x+5e^x

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