shaqadry
integrate x(1+2x)^5 dx



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ash2326
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\[\int x(1+2x)^5dx\]
We can expand (1+2x)^5, but that will be tiring
Do you know u substitution method ?

shaqadry
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how do i solve it by parts?

ash2326
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Not by parts, do u know usubstitution?
It'll make it easy

ash2326
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@shaqadry Put 2x+1=t
so
\[2dx=dt\]
\[dx=\frac{dt}{2}\]
Do you get this?

shaqadry
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yes!

shaqadry
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and then?

shaqadry
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wait but the question requires me to solve it by parts :/

ash2326
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Then, we will use this
\[\int uv=u\int v\int(du \int v)\]

ash2326
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Can you try, apply it here?

shaqadry
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@ash2326 which one should i equate to 'u' ? which is the better choice?

ash2326
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Equate x to u, it'll become 1 in the second part of by parts and then we find the integral easily @shaqadry

shaqadry
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okay thanks i will try to solve it!