Question

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

Answer 1

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