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Question Number 97239 by john santu last updated on 07/Jun/20

$$\int \frac{\sec {}^{3}xdx}{\sqrt{\tan x}}?$$

Commented by MJS last updated on 07/Jun/20

$$t=\sqrt{\tan x}\mathrm{leads}\mathrm{to}2\int \sqrt{t^4+1}dt\mathrm{and}\mathrm{we}\mathrm{cannot}$$$$\mathrm{solve}\mathrm{this}\mathrm{using}\mathrm{elementary}\mathrm{calculus}$$

Commented by john santu last updated on 07/Jun/20

yes, i can't solve that integral

Commented by MJS last updated on 07/Jun/20

$$\mathrm{Wolfram}\mathrm{Alpha}\mathrm{can}\mathrm{solve}\mathrm{it},\mathrm{I}\mathrm{think}\mathrm{we}\mathrm{can}$$$$\mathrm{try}\mathrm{to}\mathrm{comprehend}$$$$\int \sqrt{x^4+1}dx=$$$$=\frac{1}{3}x\sqrt{x^4+1}-\frac{2\sqrt{\mathrm{i}}}{3}\mathrm{F}(\mathrm{i}{\sinh }^{-1}\left(x\sqrt{\mathrm{i}}\right)\mid -1)+C$$$$\mathrm{look}\mathrm{up}\mathrm{the}\mathrm{definition}\mathrm{of}F(\phi \mid m)$$$$\mathrm{sorry}\mathrm{I}\mathrm{have}\mathrm{got}\mathrm{no}\mathrm{time}\mathrm{today}$$

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