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Core 3 integration by substitution question

Integrate sinxcosx (1+cosx)^4 dx

let U= 1+cosx

I got the answer as 1/5 (1+cosx)^5 - 1/6 (1+cosx)^6 + C

Is this correct?

Reply 1

joostan

Original post by MSI_10

Integrate sinxcosx (1+cosx)^4 dx

let U= 1+cosx

I got the answer as 1/5 (1+cosx)^5 - 1/6 (1+cosx)^6 + C

Is this correct?

It's the same as what I get. . .

yes

Yay

Original post by MSI_10

Yay

You can always do a quick check by differentiating the result you obtained:

d/dx [1/5 (1+cosx)^5 - 1/6 (1+cosx)^6 + C ]

= (-sinx)*(1+cosx)^4 - (-sinx)*(1+cosx )^5

= (-sinx)*(1+cosx)^4 + (sinx)*(1+cosx )^5

= (sinx)*(1+cosx)^4 [ -1+(1+cos x)]

= (sinx)*(1+cosx)^4 *(cos x)

= sinxcosx (1+cosx)^4 (shown)

So perfecto my friend, an integration problem well solved. Peace.