Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 128529 by bramlexs22 last updated on 08/Jan/21

Commented by liberty last updated on 08/Jan/21

considering (d/dx)((u/v))=((u′v−uv′)/v^2 ) obvious v=2+3cos x and 3+2cos x=u′(2+3cos x)−u(−3sin x) ⇒2cos x+3=2u′+3u′cos x+3u sin x check u = sin x ⇒ u′(2+3cosx)+3u sin x= 2cos x+3cos^2 x+3sin^2 x = 2cos x+3 (valid) therefore ∫ ((3+2cos x)/((2+3cos x)^2 )) dx=((sin x)/(2+3cos x))

$$\mathrm{considering}\:\frac{\mathrm{d}}{\mathrm{dx}}\left(\frac{\mathrm{u}}{\mathrm{v}}\right)=\frac{\mathrm{u}'\mathrm{v}−\mathrm{uv}'}{\mathrm{v}^{\mathrm{2}} } \\ $$$$\:\mathrm{obvious}\:\mathrm{v}=\mathrm{2}+\mathrm{3cos}\:\mathrm{x}\:\mathrm{and}\:\mathrm{3}+\mathrm{2cos}\:\mathrm{x}=\mathrm{u}'\left(\mathrm{2}+\mathrm{3cos}\:\mathrm{x}\right)−\mathrm{u}\left(−\mathrm{3sin}\:\mathrm{x}\right) \\ $$$$\Rightarrow\mathrm{2cos}\:\mathrm{x}+\mathrm{3}=\mathrm{2u}'+\mathrm{3u}'\mathrm{cos}\:\mathrm{x}+\mathrm{3u}\:\mathrm{sin}\:\mathrm{x} \\ $$$$\mathrm{check}\:\mathrm{u}\:=\:\mathrm{sin}\:\mathrm{x}\:\Rightarrow\:\mathrm{u}'\left(\mathrm{2}+\mathrm{3cosx}\right)+\mathrm{3u}\:\mathrm{sin}\:\mathrm{x}=\: \\ $$$$\mathrm{2cos}\:\mathrm{x}+\mathrm{3cos}^{\mathrm{2}} \:\mathrm{x}+\mathrm{3sin}^{\mathrm{2}} \mathrm{x}\:=\:\mathrm{2cos}\:\mathrm{x}+\mathrm{3}\:\left(\mathrm{valid}\right)\:\: \\ $$$$\mathrm{therefore}\:\int\:\frac{\mathrm{3}+\mathrm{2cos}\:\mathrm{x}}{\left(\mathrm{2}+\mathrm{3cos}\:\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{dx}=\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{2}+\mathrm{3cos}\:\mathrm{x}}\: \\ $$$$ \\ $$

Commented by SLVR last updated on 08/Jan/21

sir.. just multiply and divide with Cosec^2 x will give the same answer .

$${sir}..\:{just}\:{multiply}\:{and}\:{divide}\:{with}\:{Cosec}^{\mathrm{2}} {x}\: \\ $$$${will}\:{give}\:{the}\:{same}\:{answer}\:. \\ $$

Answered by SLVR last updated on 08/Jan/21

$$ \\ $$

Commented by bramlexs22 last updated on 08/Jan/21

what ?

$$\mathrm{what}\:? \\ $$

Commented by SLVR last updated on 08/Jan/21

i hope are agreed with the solution

$${i}\:{hope}\:{are}\:{agreed}\:{with}\:{the}\:{solution} \\ $$

Commented by john_santu last updated on 08/Jan/21

what your solution?

$$\mathrm{what}\:\mathrm{your}\:\mathrm{solution}? \\ $$

Commented by SLVR last updated on 09/Jan/21

Commented by SLVR last updated on 09/Jan/21

sorry... i didnot observed uploading part

$${sorry}...\:{i}\:{didnot}\:{observed}\:{uploading}\:{part} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com