Mathematics

Integrate the following function with respect to $$x$$
$$\dfrac{(x+1).(x+\log{x})^{4}}{3x}$$


SOLUTION
According to question,
Let,
$$x+logx=t$$

$$\implies( 1+\dfrac{1}{x})dx=dt$$

$$\implies( \dfrac{1+x}{x})dx=dt$$

Substitute this values, we get

$$\int \dfrac{t^4}{3}dt$$

$$\implies  \dfrac{t^5}{3\times5}+C$$

$$\implies \dfrac{(x+logx)^5}{15}+C$$
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Subjective Medium Published on 17th 09, 2020
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