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Category: Integration

dx-1-tan-x-

Question Number 12766 by Joel577 last updated on 01/May/17 $$\int\:\frac{{dx}}{\mathrm{1}\:+\:\mathrm{tan}\:{x}} \\ $$ Answered by sma3l2996 last updated on 01/May/17 $${t}={tanx}\Rightarrow{dt}=\left(\mathrm{1}+{tan}^{\mathrm{2}} {x}\right){dx} \\ $$$${dx}=\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{2}} } \\…

sec-x-tan-2-x-dx-

Question Number 12768 by Joel577 last updated on 01/May/17 $$\int\:\frac{\mathrm{sec}\:{x}}{\mathrm{tan}^{\mathrm{2}} \:{x}}\:{dx} \\ $$ Answered by prakash jain last updated on 01/May/17 $$\int\:\frac{\mathrm{sec}\:{x}\centerdot\mathrm{cos}^{\mathrm{2}} {x}}{\mathrm{sin}^{\mathrm{2}} {x}}\:\mathrm{d}{x} \\…

e-3-e-2-1-x-log-x-dx-

Question Number 12744 by tawa last updated on 30/Apr/17 $$\int_{\:\mathrm{e}^{−\mathrm{3}} } ^{\:\mathrm{e}^{−\mathrm{2}} } \:\:\frac{\mathrm{1}}{\left(\mathrm{x}\right)\mathrm{log}\left(\mathrm{x}\right)}\:\mathrm{dx}\:\:=\:\:? \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 30/Apr/17 $${logx}={t}\Rightarrow{dx}/{x}={dt} \\…

Prove-that-dx-x-1-2-x-2-2x-2-x-2-2x-2-x-1-C-

Question Number 12742 by Joel577 last updated on 30/Apr/17 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\int\:\frac{{dx}}{\left({x}\:+\mathrm{1}\right)^{\mathrm{2}} \:\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:+\mathrm{2}}}\:=\:\frac{−\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:+\:\mathrm{2}}}{{x}\:+\:\mathrm{1}}\:+\:{C} \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 30/Apr/17 $$\frac{\mathrm{1}}{{x}+\mathrm{1}}={t}\Rightarrow\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}}…