The integral

Engineering

Mathematics

Integration of Miscellaneous Functions

Question

The integral $\int \frac{dx}{x^{2} {(x^{4} + 1)}^{\frac{3}{4}}} equals$

$- {(x^{4} + 1)}^{\frac{1}{4}} + c$

${(x^{4} + 1)}^{\frac{1}{4}} + c$

$- {(\frac{x^{4} + 1}{x^{4}})}^{\frac{1}{4}} + c$

${(\frac{x^{4} + 1}{x^{4}})}^{\frac{1}{4}} + c$

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$I = \int \frac{dx}{x^{5} {(1 + \frac{1}{x^{4}})}^{\frac{3}{4}}}$

$Put (1 + \frac{1}{x^{4}}) = t \Rightarrow \frac{- 4}{x^{5}} dx = dt$

$∴ I = \frac{- 1}{4} \int t^{\frac{- 3}{4}} dt = - {(\frac{x^{4} + 1}{x^{4}})}^{\frac{1}{4}} + c$