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Category: Integration

tanx-dx-

Question Number 6220 by sanusihammed last updated on 18/Jun/16 $$\int\sqrt{{tanx}}\:\:{dx}\: \\ $$ Answered by malwaan last updated on 19/Jun/16 $$\int\sqrt{{tanx}}\:{dx}=\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{2}}}\left(\mathrm{2}{tan}^{−\mathrm{1}} \left(\mathrm{1}+\sqrt{\mathrm{2}{tanx}}\right)\right. \\ $$$$−\mathrm{2}{tan}^{−\mathrm{1}} \left(\mathrm{1}−\sqrt{\mathrm{2}{tanx}}\right) \\…

5-2cos-2x-4-2sin-2x-dx-

Question Number 137285 by bemath last updated on 31/Mar/21 $$\int\:\frac{\mathrm{5}+\mathrm{2cos}\:\mathrm{2x}}{\mathrm{4}+\mathrm{2sin}\:\mathrm{2x}}\:\mathrm{dx}\: \\ $$ Answered by EDWIN88 last updated on 31/Mar/21 $$\mathrm{E}=\int\:\frac{\mathrm{2cos}\:\mathrm{2x}}{\mathrm{4}+\mathrm{2sin}\:\mathrm{2x}}\:\mathrm{dx}\:+\:\int\:\frac{\mathrm{5}}{\mathrm{4}+\mathrm{2sin}\:\mathrm{2x}}\:\mathrm{dx} \\ $$$$\mathrm{E}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{d}\left(\mathrm{4}+\mathrm{2sin}\:\mathrm{2x}\right)}{\mathrm{4}+\mathrm{2sin}\:\mathrm{2x}}\:+\:\int\:\frac{\mathrm{5}}{\mathrm{4}+\mathrm{2sin}\:\mathrm{2x}}\:\mathrm{dx} \\ $$$$\mathrm{E}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mid\mathrm{4}+\mathrm{2sin}\:\mathrm{2x}\:\mid\:+\:\int\:\frac{\mathrm{5}}{\mathrm{4}+\mathrm{2sin}\:\mathrm{2x}}\:\mathrm{dx}\: \\…

tanx-dx-

Question Number 6214 by sanusihammed last updated on 18/Jun/16 $$\int\sqrt{{tanx}}\:\:{dx}\: \\ $$ Commented by nburiburu last updated on 24/Jun/16 $${by}\:\:{substitution} \\ $$$${t}=\sqrt{{tan}\:{x}}\Rightarrow{t}^{\mathrm{2}} =\:{tan}\:{x} \\ $$$$\mathrm{2}{t}\:{dt}\:=\:{sec}^{\mathrm{2}}…

Evaluate-0-1-x-3x-4-dx-

Question Number 6204 by sanusihammed last updated on 18/Jun/16 $${Evaluate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}\left(\sqrt{\mathrm{3}{x}\:−\:\mathrm{4}}\right)\:{dx} \\ $$ Answered by FilupSmith last updated on 18/Jun/16 $${u}=\mathrm{3}{x}−\mathrm{4}\:\Rightarrow\:{du}=\mathrm{3}{dx}\:\rightarrow\:{dx}=\frac{\mathrm{1}}{\mathrm{3}}{du} \\ $$$${x}=\frac{\mathrm{1}}{\mathrm{3}}\left({u}+\mathrm{4}\right) \\…