Integrate \(3x^2 (cos⁡x^3+8)\).

Category: QuestionsIntegrate \(3x^2 (cos⁡x^3+8)\).
Editor">Editor Staff asked 11 months ago

Integrate \(3x^2 (cos⁡x^3+8)\).
 
(a) \(sin⁡x^3-8x^3+C\)
 
(b) \(sin⁡x^3+8x^3+C\)
 
(c) –\(sin⁡x^3+8x^3+C\)
 
(d) \(sin⁡x^3-x^3+C\)
 
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1 Answers
Editor">Editor Staff answered 11 months ago

The correct answer is (b) \(sin⁡x^3+8x^3+C\)
 
Easy explanation: By using the method of integration by substitution,
 
Let x^3=t
 
Differentiating w.r.t x, we get
 
3x^2 dx=dt
 
\(\int 3x^2 \,(cos⁡x^3+8) \,dx=\int (cos⁡t+8)dt\)
 
\(\int (cos⁡t+8) dt=sin⁡t+8t\)
 
Replacing t with x^3,we get
 
\(\int 3x^2 (cos⁡x^3+8) dx=sin⁡x^3+8x^3+C\)