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integrate e cosx (xsin 3 x + cosx)/sin 2 x w.r.t x

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

Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
10 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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