Thread: 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!

can you finish?

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

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

what is the antiderivative of ?

what is the antiderivative of ?

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) ??

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 ...

Thanks skeeter, big help, I know I need practice

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.

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

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

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