I have a problem like this : x(2x+1)1/3
We need to find the antiderivative.
The step I don't understand, which is in the book, is this:
du=(2x+1)1/3
That would be 2/3(2x+1)2/3 because u=(2x+1)1/3
That makes sense to me, as it is the derivative of (2x+1)1/3.
Then we have x=u3/2-1/2, which makes sense.
However, I then see where it says:
x(2x+1)1/3= 3/2 u3(u3/2-1/2)The only part that does not make sense to me is how did they get the 3/2u3?
I would think that derivative of u3/2-1/2 would be 3/2u2
After this step, the rest of the problem is easily understood.
The answer comes out to be 3/112(2x+1)4/3(8x-3)+C
Any help is appreciated!
We need to find the antiderivative.
The step I don't understand, which is in the book, is this:
du=(2x+1)1/3
That would be 2/3(2x+1)2/3 because u=(2x+1)1/3
That makes sense to me, as it is the derivative of (2x+1)1/3.
Then we have x=u3/2-1/2, which makes sense.
However, I then see where it says:
x(2x+1)1/3= 3/2 u3(u3/2-1/2)The only part that does not make sense to me is how did they get the 3/2u3?
I would think that derivative of u3/2-1/2 would be 3/2u2
After this step, the rest of the problem is easily understood.
The answer comes out to be 3/112(2x+1)4/3(8x-3)+C
Any help is appreciated!