-dx-x5-61-5x1-3-1-4x1-3 equals

The correct option is C 6 cot^ 1 (√(1+4x^1/3/x^1/3) )+c Put x^1/3=t^2 ⇒ Given integration =6∫dt(1+5t^2)√(1+4t^2) Let 4+1t^2=u^2 ...

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Integration of Trigonometric Functions

∫dx/x5/61+5x1...

Question

$\int \frac{d x}{x^{5 / 6} (1 + 5 x^{1 / 3}) \sqrt{1 + 4 x^{1 / 3}}}$ equals

6 t a n^{- 1} (\sqrt{\frac{1 + 4 x^{1 / 3}}{x^{1 / 3}}}) + c

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3 l n ∣ ∣ ∣ \frac{1 + \sqrt{4 + x^{- 1 / 3}}}{1 - \sqrt{4 + x^{- 1 / 3}}} ∣ ∣ ∣ + c

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6 c o t^{- 1} (\sqrt{\frac{1 + 4 x^{1 / 3}}{x^{1 / 3}}}) + c

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3 l n ∣ ∣ ∣ \frac{1 - \sqrt{4 + x^{- 1 / 3}}}{1 - \sqrt{4 - x^{- 1 / 3}}} ∣ ∣ ∣ + c

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