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tanx-dx-




Question Number 6220 by sanusihammed last updated on 18/Jun/16
∫(√(tanx))  dx
$$\int\sqrt{{tanx}}\:\:{dx}\: \\ $$
Answered by malwaan last updated on 19/Jun/16
∫(√(tanx)) dx=(1/(2(√2)))(2tan^(−1) (1+(√(2tanx)))  −2tan^(−1) (1−(√(2tanx)))  +log((√(2tanx))−tanx−1)  −log((√(2tanx))+tanx+1))
$$\int\sqrt{{tanx}}\:{dx}=\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{2}}}\left(\mathrm{2}{tan}^{−\mathrm{1}} \left(\mathrm{1}+\sqrt{\mathrm{2}{tanx}}\right)\right. \\ $$$$−\mathrm{2}{tan}^{−\mathrm{1}} \left(\mathrm{1}−\sqrt{\mathrm{2}{tanx}}\right) \\ $$$$+{log}\left(\sqrt{\mathrm{2}{tanx}}−{tanx}−\mathrm{1}\right) \\ $$$$\left.−{log}\left(\sqrt{\mathrm{2}{tanx}}+{tanx}+\mathrm{1}\right)\right) \\ $$
Answered by prakash jain last updated on 20/Jun/16
Please see answer to Question 119.
$$\mathrm{Please}\:\mathrm{see}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{Question}\:\mathrm{119}. \\ $$

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