Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
0 votes

Integrate : $\int 5x^2 \tan ^2 (6x^3) dx$

$(a)\;cos (6x^3)+c \qquad(b)\;\sin (6x^3)+c \qquad(c)\;\frac{5}{18} [\cot (6x^3)-(6x^3)]+c \qquad (d)\;\frac{5}{18} [\tan (6x^3)-(6x^3)]+c$
Can you answer this question?

1 Answer

0 votes
$6x^3=t$=> differentiate with respect to x
$18 x ^2 dx =dt$
=> $\int \large\frac{5}{18}$$ \tan ^2 t dt$
=> $\int \large\frac{5}{18} $$(\sec ^2 t -1)$$dt$
=> $ \large\frac{5}{18} $$(\sec ^2 t -1)$$dt$
=> $\large\frac{5}{18} $$(\tan t -t)+c$
$ \large\frac{5}{18}$$ [\tan (6x^3)-(6x^3)]+c$
Hence d is the correct answer.
answered Dec 24, 2013 by meena.p
edited Mar 13, 2014 by balaji.thirumalai
Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App