First slide
Methods of integration
Question

If f(x)=x,g(x)=ex1 and h(x)=tan1x 

then the anti derivative of (f o g) (x) is 

Moderate
Solution

I=ex1dx

Put ex1=t2, so that  exdx=2tdt

I=t2tt2+1dt=2t2+11t2+1dt=2ttan1t+C=2ex1tan1ex1+C

=2[( fog )(x)( hofog )(x)]+C.

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