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integrate ecosx(xsin3x + cosx)/sin2x w.r.t x

suchita undare , 13 Years ago
Grade 12th Pass
anser 1 Answers
Ashwin Muralidharan IIT Madras

Last Activity: 13 Years ago

Hi Suchita,

 

Split this integral as ∫ecosx(xsinx + cotx cosecx) dx

= {∫x ecosxsinx dx} + {∫ecosx cotx cosecx dx} ----------- then integrate both by parts seperately.

= {x(-ecosx) - ∫(-ecosx) dx} + {ecosx(-cosecx) - ∫(-cosecx) ecosx(-sinx) dx}

= -xecosx + ∫(ecosx) dx - ecosxcosecx - ∫(ecosx) dx ---------- (Now ∫ecosx dx cancels with -∫ecosx dx)

= -xecosx - ecosxcosecx + constant.

 

And that solves the problem.

 

Hope that helps.

 

All the best.

Regards,

Ashwin (IIT Madras).

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