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Write a value of inte^2x^(2+lnx)\ dx...

Write a value of `inte^2x^(2+lnx)\ dx`

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Solution:
I=`\int e^{2 x^{2}+\ln x} d x \Rightarrow x e^{2 x^{2}} d x`
Let `x^{2}=t`. Then
`2 x d x=d t`
`\Rightarrow I=\frac{1}{2} \int e^{2 t} d t=\frac{e^{2 t}}{4}+c=\frac{e^{2 x^{2}}}{4}+c`
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