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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)+CI got this question during a job interview.Question is taken from Methods of Integration-2 in section Integrals of Mathematics – Class 12

Answer» 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

=sin⁡t+C

Replacing w.r.t x, we get

∴∫ 2x cos⁡(x^2+3) dx=sin⁡(x^2+3)+C


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