Evaluate the following indefinite integral: int(x^3*sin(2x+1) dx)

Question

zepdrix · Answer

$$\large \int\limits x^3 \sin(2x+1) \; dx$$Hmmmm, it looks like you're going to have to do integration by parts.
What method are you more comfortable with? Writing out the U and DV, or using the tabular method?
I'm not very familiar with the tabular method, but it might help a bit here since we have to integrate like 4 times.

anonymous · Answer

Yeah, I use tabular.  Which basically says I multiply x^3 by (d/dx(sin(2x+1))) then add that to the multiplication of d/dx(x^3) and  (d/dx(d/dx(sin(2x+1)))) ... (a  table of dirivatives works wonders for this type of problem)
I know the steps, but I'm still getting the wrong answer.   

(d/dx(sin(2x+1))) is 2sin(2x+1), correct?  I think my professor has it as (1/2)sin(2x+1)...

anonymous · Answer

What I said was just the first step... you keep interchanging between adding and subtracting the multiplications, I Know.

zepdrix · Answer

You don't want to take the derivative of the sine function.
You want to instead differentiate the power of x, see how it will deteriorate as you take the derivative over and over?

The sine is the one you want to integrate, that's where the 1/2 is coming from each time you integrate.

anonymous · Answer

OH.  That's right.  Okay, by integrating sin function I have the right answer... Thanks for the help.

anonymous · Answer

A solution is attached.