Category: Integration

Question Number 102058 by Dwaipayan Shikari last updated on 06/Jul/20 $${\int }_0^1\frac{sin\left(logx\right)}{logx}dx$$ Answered by prakash jain last updated on 06/Jul/20 $${x}={e}^{{u}} \…

Question Number 102043 by Dwaipayan Shikari last updated on 06/Jul/20 $$\int e^{\sqrt{ax+b}}dx$$ Commented by Dwaipayan Shikari last updated on 06/Jul/20 $$\frac{\mathrm{2}}{{a}}\int{e}^{{u}} {udu}\:\:\:\:\:\:\:\:\:\:\:\:\:\left\{{suppose}\:{ax}+{b}={u}^{\mathrm{2}} \right.…

Question Number 36491 by rahul 19 last updated on 02/Jun/18 Answered by MJS last updated on 08/Jun/18 $$\mathrm{just}\mathrm{differentiate}\mathrm{the}\mathrm{following}\mathrm{term}:$$$$\pm \frac{1}{{(\sec x+\tan x)}^{\frac{11}{2}}}(\frac{1}{11}\pm \frac{1}{7}{(\sec x+\tan x)}^2)$$$$\mathrm{write}\:\mp\:\mathrm{for}\:\mathrm{changing}\:\mathrm{signs}.\:\mathrm{it}'\mathrm{s}\:\mathrm{faster} \…

Question Number 36459 by rahul 19 last updated on 02/Jun/18 $$\int {\mathrm{e}}^{\tan \theta }(\sec \theta -\sin \theta )\mathrm{d}\theta =?$$ Answered by ajfour last updated on 02/Jun/18 $$let\tan \theta =t$$$$\Rightarrow\:{I}=\int{e}^{{t}} \left(\mathrm{sec}\:\theta−\mathrm{sin}\:\theta\right)\mathrm{cos}\:^{\mathrm{2}}…

Question Number 36444 by rahul 19 last updated on 02/Jun/18 $$\int \frac{\mathrm{d}x}{(2x-7)\sqrt{(x-3)(x-4)}}=?$$ Commented by math1967 last updated on 02/Jun/18 $$let2x-7=\frac{1}{z}\therefore 2dx=-\frac{dz}{z^2}$$$$−\int\frac{{dz}}{\mathrm{2}{z}^{\mathrm{2}} ×\frac{\mathrm{1}}{{z}}\sqrt{\frac{\left(\mathrm{1}+{z}\right)}{\mathrm{2}{z}}×\frac{\left(\mathrm{1}−{z}\right)}{\mathrm{2}{z}}}}…