Step-by-step explanation:

<u>Given integral is</u>

<u>To evaluate this integral, we have to first remove the fractional exponents from the integrand.</u>
<h3 /><h3 /><h3>So, we substitute</h3>
![\sf{x = {y}^{4} \: \: \: \: \: \: \: \: \: \: \bigg[\rm\implies \:y = {\bigg(x\bigg) }^{\dfrac{1}{4} }\bigg] }](https://tex.z-dn.net/?f=%20%5Csf%7Bx%20%3D%20%7By%7D%5E%7B4%7D%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5Cbigg%5B%5Crm%5Cimplies%20%5C%3Ay%20%3D%20%7B%5Cbigg%28x%5Cbigg%29%20%7D%5E%7B%5Cdfrac%7B1%7D%7B4%7D%20%7D%5Cbigg%5D%20%7D)
So, on substituting these values, above integral can be rewritten as


To evaluate this integral further, <u>we substitute</u>




<h3>So, on substituting these values in above integral, we get</h3>


![\rm \: = \: \dfrac{4}{3} \displaystyle\int\rm \bigg[1 - \frac{1}{t} \bigg] \:](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Cdfrac%7B4%7D%7B3%7D%20%5Cdisplaystyle%5Cint%5Crm%20%5Cbigg%5B1%20-%20%5Cfrac%7B1%7D%7Bt%7D%20%5Cbigg%5D%20%5C%3A%20)


![\rm \: = \: \dfrac{4}{3} \bigg[ {\bigg(x \bigg) }^{\dfrac{3}{4} } + 1 \: - \: log \bigg| {\bigg(x\bigg) }^{\dfrac{3}{4} } + 1\bigg|\bigg] \:](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Cdfrac%7B4%7D%7B3%7D%20%5Cbigg%5B%20%7B%5Cbigg%28x%20%5Cbigg%29%20%7D%5E%7B%5Cdfrac%7B3%7D%7B4%7D%20%7D%20%2B%201%20%5C%3A%20-%20%5C%3A%20log%20%5Cbigg%7C%20%7B%5Cbigg%28x%5Cbigg%29%20%7D%5E%7B%5Cdfrac%7B3%7D%7B4%7D%20%7D%20%2B%201%5Cbigg%7C%5Cbigg%5D%20%5C%3A%20)
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<h2>ADDITIONAL INFORMATION</h2>
