∫ xe x cosx dx= f(x)+c, then find f(x).

∫ xex cosx dx= f(x)+c, then find f(x).


1 Answers

Rathod Shankar AskiitiansExpert-IITB
69 Points
13 years ago


integral by parts take  x and ex cosx as two parts

\int f g\, dx = f \int g\, dx - \int \left ( f' \int g\,dx \right )\, dx.\!

take f=x   and g=ex cosx
here iam giving method for integration for ex cosx ...i think u can solve now right. do practice so that u can get more concept

\int e^{x} \cos (x) \, dx\!
u = \cos(x) \Rightarrow du = -\sin(x)\,dx
dv = e^x \, dx \Rightarrow v = \int e^x \, dx = e^x
\int e^{x} \cos (x) \, dx = e^{x} \cos (x) + \int e^{x} \sin (x) \, dx.\!
u = \sin(x) \Rightarrow du = \cos(x)\, dx
dv = e^x \, dx \Rightarrow v = \int e^x \, dx = e^x
\int e^x \sin (x) \, dx = e^x \sin (x) - \int e^x \cos (x) \,dx

Putting these together,

\int e^x \cos (x) \,dx = e^x \cos (x) + e^x \sin (x) - \int e^x \cos (x) \, dx.
2 \int e^{x} \cos (x) \, dx = e^{x} ( \sin (x) + \cos (x) ) + C\!
\int e^x \cos (x) \,dx = {e^x ( \sin (x) + \cos (x) ) \over 2} + C'\!

Now you can win exciting gifts by answering the questions on
Discussion Forum. So help discuss any query on askiitians forum and
become an Elite Expert League askiitian.
Now you score 5+15 POINTS by uploading your Pic and Downloading the
Askiitians Toolbar : Click here to download the toolbar..

Think You Can Provide A Better Answer ?


Get your questions answered by the expert for free