arsh125
\[\int\limits_{1}^{6} x^2/\sqrt{x+3}\]



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arsh125
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how do i evaluate that integral

RadEn
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int by subs, let u=x+3

UnkleRhaukus
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\[\int_1^6\frac{x^2}{\sqrt{x+3}}\text dx\]
\(u=x+3\)
\(\frac{\text du}{\text dx}=1\)
\(\text du=\text dx\)
\[=\int_1^6\frac{(u3)^2}{\sqrt{u}}\text du\]

UnkleRhaukus
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\[=\int_1^6\frac{u^26u+9}{\sqrt{u}}\text du\]
\[=\int_1^6\frac{u^2}{\sqrt{u}}\text du6\int_1^6\frac{u}{\sqrt{u}}\text du+9\int_1^6\frac{1}{\sqrt{u}}\text du\]

lgbasallote
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^?

UnkleRhaukus
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no?