# Math Help - Help with a U substitution problem.

1. ## Help with a U substitution problem.

I can't figure out how to do this but Ive been assured its easily doable.

Calculate: (int) 2x(4x+7)8 dx

So I'm assuming we try to get 4x on its own and find 2x in terms of u?

A solution to this would help me heaps here I just cant see it!

2. ## Re: Help with a U substitution problem.

$\int 2x(4x+7)^8 \, dx$

$u = 4x+7$

$x = \frac{u-7}{4}$

$dx = \frac{du}{4}$

$\int 2x(4x+7)^8 \, dx$

$\int \frac{u-7}{8} \cdot u^8 \, du$

$\frac{1}{8} \int u^9 -7u^8 \, du$

can you finish?

3. ## Help with a U substitution problem.

Thanks! Im not sure if I can Im really having trouble with integration. Would appreciate the rest.

4. ## Re: Help with a U substitution problem.

If you're at the level of doing integrals by substitution, then this should be basic stuff.

what is the antiderivative of $u^9$ ?

what is the antiderivative of $u^8$ ?

5. ## Re: Help with a U substitution problem.

I havent studied math for about 10 years so i struggle with the basic stuff.

so antiderivative of u^9=1/10u^10
and for u^8=1/9u^9

so 1/8 (1/10 u^10 - 7/9 u^9) ??

6. ## Re: Help with a U substitution problem.

Originally Posted by camjerlams
I havent studied math for about 10 years so i struggle with the basic stuff.

so antiderivative of u^9=1/10u^10
and for u^8=1/9u^9

so 1/8 (1/10 u^10 - 7/9 u^9) + C
was that so difficult?

now finish it by back-substituting (4x+7) for u ...

7. ## Re: Help with a U substitution problem.

Thanks skeeter, big help, I know I need practice

8. ## Re: Help with a U substitution problem.

note you don't have to resort to u-substitution, you COULD just multiply out (4x+7)8, and then multiply every term by 2x, and then integrate term-by term. this is kind of "the hard way", u-substitutions are meant to make your life EASIER (short-cuts are good, right?).

linear substitutions u = ax+b are always "do-able", we just have a "fudge factor" of a constant to worry about:

du = a dx, so

dx = (1/a) du <--take the 1/a outside the integral sign.

9. ## Re: Help with a U substitution problem.

so, 1/8((1/10u^10) - (7/9u^9))

=1/8((4x+7)^10/10 - 7/9(4x+7)^9)

10. ## Re: Help with a U substitution problem.

don't forget to add the constant of integration....