Integration question

[vchs]

Can anyone help me step-by-step with ∫ -4(1 - 1/2x)^7 dx?

[The Cat In The Hat]

Can anyone help me step-by-step with ∫ -4(1 - 1/2x)^7 dx?

Maybe try putting this on the Methods Question Thread? It'll probably get more people looking at it...

[eloisegrace]

Correct me if I am wrong but I think this question is out of the scope of the methods course as it is a composite function (if that makes sense).

The only way this might be possible is if the first part of the question said differentiate this and hence antidifferentiate this.

[whys]

Correct me if I am wrong but I think this question is out of the scope of the methods course as it is a composite function (if that makes sense).

The only way this might be possible is if the first part of the question said differentiate this and hence antidifferentiate this.

Since the function inside the brackets is a linear function you can use the antichain rule to antidiff it.

[S_R_K]

Correct me if I am wrong but I think this question is out of the scope of the methods course as it is a composite function (if that makes sense).

The only way this might be possible is if the first part of the question said differentiate this and hence antidifferentiate this.

It's definitely within the scope of Methods, although how likely it is to appear depends on what the question actually is. The typesetting of the question is ambiguous, it's unclear if "1/2x" is meant to be (1/2)x or 1/(2x).

If it's the former, then it's easily antidifferentiated using the rule for (ax + b)^n, which is on the formula sheet. If it's the latter, then expand using binomial theorem and anti-differentiate term by term, which is slightly tedious but straightforward.

[1729]

Can anyone help me step-by-step with ∫ -4(1 - 1/2x)^7 dx?

Did you mean

Or

Use parentheses if its the first, your only option is probably just to expand it and integrate each term; if its the second, use a u-sub of u=1-(1/2)x

EDIT: S_R_K and whys has beaten me

[eloisegrace]

Sorry for the confusion, I interpreted it as 1/2x^-1 instead of 1/2x...