$∫\sin^4x\cos^5x\,dx \ \sin x=u$ substitution

Asked Sep 22 '21 at 19:02

Active Sep 22 '21 at 19:07

Viewed 50 times

I am reading this.

And hour ago I posted question of $$\int \sin^4x \cos^5xdx$$ Solution was to do $\sin x=u$ substitution.

But if you follow what wiki says $$\int \sin^4x\cos^5x\,dx=\int \sin^4(-x)\cos^5(-x)dx$$ so you should do $\cos x=u$ substitution.

Could you please explain this point? And sorry if this is trivial question.

edited Sep 22 '21 at 19:07

Тyma Gaidash

asked Sep 22 '21 at 19:02

unit 1991

@TymaGaidash Yes! – unit 1991 Sep 22 '21 at 19:04
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Does this answer your question? Find $\int \sin^4(x)\cos^5(x)dx$. This was a redone comment. – Тyma Gaidash Sep 22 '21 at 19:12
I suggest you add a comment asking José Carlos Santos about your question in the previous question. – Тyma Gaidash Sep 22 '21 at 19:14
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Unfortunately the Wiki article is misleading. You need to take into account $dx$. See this answer: https://math.stackexchange.com/a/3128181/469083 Basically, you substitute $x$ for $-x$ in the $dx$ as well – Vasili Sep 22 '21 at 19:14
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Indeed, you accepted the answer to the first time you asked this. It is inappropriate to ask the same question 34 minutes after your first question. – amWhy Sep 22 '21 at 19:16
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@unit1991 Check this link https://newbedev.com/formulation-of-bioche-s-rules-in-familiar-notation – Vasili Sep 22 '21 at 19:21
@Vasya Thank you I will take a look at it. – unit 1991 Sep 22 '21 at 19:25

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