Evaluate the integral using integration by parts where possible
(x^2 +9)e^3x+8 dx

Question

Evaluate the integral using integration by parts where possible
(x^2 +9)e^3x+8 dx

zepdrix · Answer

$$\large \int\limits (x^2+9)e^{3x+8}\;dx$$

So is this what we're dealing with?
Your exponent doesn't have brackets, so I just wanted to make sure.

anonymous · Answer

yes

zepdrix · Answer

See how we have a `polynomial` and an `exponential`?
Think about the properties of those two ..things.

What happens when you differentiate a polynomial over and over?
It will decrease in degree right? The powers will keep shrinking until nothing is left.

The exponential however will stay the same, (but maybe we end up with some extra junk due  to the chain rule).

We want our U to be the polynomial.
It will decrease in degree, until it eventually deteriorates, leaving us with an easy integral.

$$\large u=x^2+9 \qquad \qquad dv=e^{3x+8}dx$$
Can you find the $\large du$ and $\large v$ ?

anonymous · Answer

du=2x right

anonymous · Answer

how do I find v

zepdrix · Answer

Do you know how to integrate this?
$$\large \int\limits e^{3x}dx$$

anonymous · Answer

no is it 3e^x

anonymous · Answer

(1/3)*e^(3x);

anonymous · Answer

is this how I set it up (x^2+9)1/3e^3x -1/3e^3x (2x)

anonymous · Answer

first part is (x^2+9)*(1/3)*e^(3x+8)

anonymous · Answer

in the second part you must using integration by parts

anonymous · Answer

so the second part isnt 1/3e^3x (2x)

anonymous · Answer

yes, you must integrate x*e^(3x+8) by parts

anonymous · Answer

x1/3e^3x+1 ?