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Hello.how do i integrate (x^2 + 2x + 1)sqrt(4x^2 + 8x + 5)??
You have [tex]\displaystyle \begin{align*} \int{ \left( x + 1 \right) ^2 \sqrt{ 4 \left( x + 1 \right) ^2 + 1 } \, dx } \end{align*}[/tex], I would lean towards doing a substitution here...Hello.
It is possible, that there is an easier way of solving the integral. But it could also be determined:
[tex]\displaystyle \int \ (x^2+2x+1) \sqrt{4x^2+8x+5}[/tex]
[tex]\displaystyle \int \ (x+1)(x+1) \sqrt{4(x+1)^2+1}[/tex]
Under the radical, we have:[tex]\int (x^2 + 2x + 1)\sqrt{4x^2 + 8x + 5}\,dx[/tex]