self doubt

Question

How to solve these questions

$(1)$ $I=\int_{0}^{1}(xlogx)^{4}dx$

$(2)$  $I=\frac{1}{\sqrt{2\pi}}\int_{0}^{\infty}e^{\frac{-x^{2}}{8}}dx$

$(3)$  $I=\int_{0}^{\infty}x^{\frac{1}{4}}.e^{-\sqrt{x}}dx$

Comments

In 2) put $x^{2}=z$

$2x.dx=dz$

$dx=dz/2\sqrt{z}$

then put partial integration

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for Q2 it can be solved by normal distribution function here sigma =2 MU=0 put in the equation answer will be 1

for Q3 it will be solved by gamma  Function method https://study.com/academy/lesson/gamma-function-properties-examples.html

https://www.youtube.com/watch?v=tp0HiqJPh_E

for Q1 my approach is lengthy unable to get the answer   

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thanks