Integrate 2x cos⁡(x^2+3).

Category: QuestionsIntegrate 2x cos⁡(x^2+3).
Editor">Editor Staff asked 11 months ago

Integrate 2x cos⁡(x^2+3).
(a) sin⁡(x^2+3)+C
(b) sin^2⁡(x^2+3)+C
(c) cot⁡(x^2+3)+C
(d) -sin⁡(x^2+3)+C
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Question is taken from Methods of Integration-2 in section Integrals of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

Correct choice is (a) sin⁡(x^2+3)+C
To explain: ∫ 2x cos⁡(x^2+3) dx
Let x^2+3=t
Differentiating w.r.t x, we get
2x dx=dt
∫ 2x cos⁡(x^2+3) dx=∫ cos⁡t dt
Replacing w.r.t x, we get
∴∫ 2x cos⁡(x^2+3) dx=sin⁡(x^2+3)+C