Find \int 6x(x^2+6)dx.

Category: QuestionsFind \int 6x(x^2+6)dx.
Editor">Editor Staff asked 11 months ago

Find \int 6x(x^2+6)dx.
 
(a) \frac{3x^4}{2}+18x^2+C
 
(b) \frac{3x^4}{2}-18x+C
 
(c) \frac{3x^4}{2}-18x^2+C
 
(d) \frac{3x^4}{2}+x^2+C
 
I had been asked this question in final exam.
 
My query is from Methods of Integration-1 in portion Integrals of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
Interview Questions and Answers, Database Interview Questions and Answers for Freshers and Experience

1 Answers
Editor">Editor Staff answered 11 months ago

Right choice is (a) \frac{3x^4}{2}+18x^2+C
 
To explain I would say: Let x^2=t
 
Differentiating w.r.t x, we get
 
2x dx=dt
 
\int 6x(x^2+6)dx=3\int (t+6) dt
 
3\int (t+6)dt=3\left (\frac{t^2}{2}+6t\right )=\frac{3t^2}{2}+18t
 
Replacing t with x^2
 
\int 6x(x^2+6)dx=\frac{3x^4}{2}+18x^2+C