Integrate xe^2x.

Category: QuestionsIntegrate xe^2x.
Editor">Editor Staff asked 11 months ago

Integrate xe^2x.
(a) \(\frac{e^{2x}}{4} (x-\frac{1}{4})+C\)
(b) \(\frac{e^{2x}}{4} (2x-1)+C\)
(c) \(\frac{e^{2x}}{2} (2x-1)+C\)
(d) \(\frac{e^{2x}}{4} (x+1)+C\)
This question was posed to me in class test.
I’d like to ask this question from Integration by Parts in division Integrals of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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Editor">Editor Staff answered 11 months ago

The correct option is (b) \(\frac{e^{2x}}{4} (2x-1)+C\)
Explanation: By using the formula \(\int u.v \,dx=u\int \,v \,dx-\int u'(\int \,v \,dx)\) we get
\(\int xe^{2x} dx=x\int e^{2x} dx-\int (x)’\int e^{2x} \,dx\)
=\(\frac{xe^{2x}}{2}-\int 1.\frac{e^{2x}}{2} \,dx\)
=\(\frac{e^{2x}}{4} (2x-1)+C\)