Intergration help A2 maths Watch

Bertybassett
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Hello, when integrating expressions in the form (ax+b)^n, I am aware of the formula i.g. (ax+b)^n+1/n+1(a) + c . However, when you have a number multiplying the (ax+b)^n present and you "pull" it out and put it before the integration sign, I am confused what happens after. So you integrate the thing after the integration sign as normal, and then surely you would times everything by the number you just pulled out? But then why do you only times the integrated function by this and not the +c (leave the c alone)? Many thanks
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RDKGames
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(Original post by Bertybassett)
Hello, when integrating expressions in the form (ax+b)^n, I am aware of the formula i.g. (ax+b)^n+1/n+1(a) + c . However, when you have a number multiplying the (ax+b)^n present and you "pull" it out and put it before the integration sign, I am confused what happens after. So you integrate the thing after the integration sign as normal, and then surely you would times everything by the number you just pulled out? But then why do you only times the integrated function by this and not the +c (leave the c alone)? Many thanks
Yes, all you do is pull out the number outside the integration sign. You then integrate the remaining expression as normal using that formula, and then you multiply that answer through by the number you pulled out.

The '+c' part is completely irrelevant. After you integrate, you end up with an arbitrary const. of integration. You then multiply it by the number you pulled out, but it still remains as an arbitrary constant of integration. So the multiplication really has no significance/importance.
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DontJudgeImANerd
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if we let the constant were pulling out the front be 'k', then we'd have +kc.

in essence, this is what we've done, but because the kc is still just another constant, we don't bother renaming it, at the end of the day, we've still got 'integrated function' + constant
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