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\int \frac{dx}{x^{2}\left ( 1+x^{4} \right )^{3/4}} =

  • Option 1)

    \frac{-\left ( 1+x^{4} \right )^{1/4}}{x}+c

  • Option 2)

    \frac{\left ( 1+x^{4} \right )^{1/4}}{x}+c

  • Option 3)

    \frac{-\left ( 1+x^{4} \right )^{3/4}}{x}+c

  • Option 4)

    none of these

 

Answers (1)

best_answer

As we learnt

Integration by substitution -

The functions when on substitution of the variable of integration to some quantity gives any one of standard formulas.

 

 

- wherein

Since \int f(x)dx=\int f(t)dt=\int f(\theta )d\theta all variables must be converted into single variable ,\left ( t\, or\ \theta \right )

 

 

 \int \frac{dx}{x^{2}\left ( 1+x^{4} \right )^{3/4}}=\int \frac{dx}{x^{5}\left ( 1+\frac{1}{x^{4}} \right )^{3/4}}

 Put\: \: 1+\frac{1}{x^{4}}=t 

\therefore -\frac{1}{4}\int t^{-3/4}dt=-\frac{\left ( 1+x^{4} \right )^{1/4}}{x}+c


Option 1)

\frac{-\left ( 1+x^{4} \right )^{1/4}}{x}+c

Option 2)

\frac{\left ( 1+x^{4} \right )^{1/4}}{x}+c

Option 3)

\frac{-\left ( 1+x^{4} \right )^{3/4}}{x}+c

Option 4)

none of these

Posted by

gaurav

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