# 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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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
$$\int xe^{2x} dx=x\int e^{2x} dx-\int (x)’\int e^{2x} \,dx$$
=$$\frac{xe^{2x}}{2}-\int 1.\frac{e^{2x}}{2} \,dx$$
=$$\frac{xe^{2x}}{2}-\frac{e^{2x}}{4}$$
=$$\frac{e^{2x}}{4} (2x-1)+C$$