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Integration of polynomial 2.

paulmdrdo

Active member
May 13, 2013
386
3.) ∫(3+s)1/2(s+1)2ds
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
I would let:

\(\displaystyle u=s+3\,\therefore\,du=ds\)

and now we have:

\(\displaystyle \int u^{\frac{1}{2}}(u-2)^2\,du\)

Now, expand, distribute, and then apply the power rule term by term.
 

paulmdrdo

Active member
May 13, 2013
386
I would let:

\(\displaystyle u=s+3\,\therefore\,du=ds\)

and now we have:

\(\displaystyle \int u^{\frac{1}{2}}(u-2)^2\,du\)

Now, expand, distribute, and then apply the power rule term by term.
how do you get (u-2)2?
 

Sudharaka

Well-known member
MHB Math Helper
Feb 5, 2012
1,621
Hi everyone, :)

An alternative method without using substitutions is to write the integrand only using \(s+3\).

\begin{eqnarray}

\int(s+3)^{1/2}(s+1)^2\,ds&=&\int(s+3)^{1/2}(s+3-2)^2\,ds\\

&=&\int(s+3)^{1/2}\left((s+3)^2-4(s+3)+4\right)\,ds\\

&=&\int(s+3)^{5/2}\,d(s+3)-4\int(s+3)^{3/2}\,d(s+3)+4\int(s+3)^{1/2}\,d(s+3)\\

\end{eqnarray}

Hope you can continue. :)
 

Sudharaka

Well-known member
MHB Math Helper
Feb 5, 2012
1,621