Integrate(e^sinx(xcos^3x - sinx)/cos^2x)
Shree Vignesh Sundararaman , 10 Years ago
Grade 11
Discuss with colleagues and IITians> Integrate(e^sinx(xcos^3x - sinx)/cos^2x)...
1 AnswersRinkoo Gupta
Last Activity: 10 Years ago
Integral [e^sinx(xcos^3x-sinx)/cos^2x] dx
=integral e^sinx .xcosx dx-integral e^sinx.sinx/cos^2x dx
=integral e^sinx.xcosx dx-integrale^sinx.tanxsecx dx
let sinx=t in first integral then on diff w.r. to x we get cosx dx=dt
=>integrale^t.sininverset dt-integrale^sinx.tanxsecxdx
integrating by parts Taking sininverset as first function and e^t as second function in first integral and e^sinx as first function and tanxsecx as second function in second integral, we get
sininverset.e^t-integral(1/root(1-t^2) .e^t) dt-[e^sinx.secx-integral(e^sinx.cosx.secx )dx]
=e^tsininverset-integral(e^t/root(1-t^2))dt-e^sinx.secx+integral(e^sinx)dx
=xe^sinx.-integral(e^t/root(1-t^2))dt-e^sinx.secx+integral(e^sinx)dx
using sinx=t and cosxdx=dt, we get
=>xe^sinx-integral(e^sinx)dx-e^sinx.secx+integral(e^sinx) dx
=xe^sinx-e^sinx.secx +C
=(x-secx).e^sinx +C
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty
Provide a better Answer & Earn Cool Goodies
Enter text here...
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
Other Related Questions on discuss with colleagues and iitians
Are core branches(Mechanical) in Top 3 NIT worth it ?
discuss with colleagues and iitians
1 Answer Available
Last Activity: 2 Years ago
My rank in JEE Advanced 2022 is 1871. Should I go for IIT Guwahati ECE or IIT Kanpur Mechanical and try for a branch change to CS or Electrical Engineering? Is changing your branch very difficult?
discuss with colleagues and iitians
1 Answer Available
Last Activity: 2 Years ago
What awaits me after jee and do you think it's worth it?
discuss with colleagues and iitians
0 Answer Available
Last Activity: 2 Years ago
Can i sacrifice board exams for jee mains as board exams are no where valueable as cuet and other will be seen for admission
discuss with colleagues and iitians
0 Answer Available
Last Activity: 2 Years ago
Is a student studying in IGCSE syllabus eligible for taking IOQP or IOQJS?
discuss with colleagues and iitians
0 Answer Available
Last Activity: 2 Years ago