integration of x^3e^x^2
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Solution:-
Use substitution method by considering x^2=u, so that it is x dx=1/2 du.
The given integral is thus transformed to 1/2ue^u du. Now integrate it by parts to have 1/2(ue^u−e^u)+C.
Now substitute back x^2 for u, to have the Integral as
1/2(x^2e^x^2−e^x^2)+C
Use substitution method by considering x^2=u, so that it is x dx=1/2 du.
The given integral is thus transformed to 1/2ue^u du. Now integrate it by parts to have 1/2(ue^u−e^u)+C.
Now substitute back x^2 for u, to have the Integral as
1/2(x^2e^x^2−e^x^2)+C
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