Most Important Selected Qs for JEE AdvancedMathematicsIndefinite Integration

If I= x^5 d x 1+x^3 , then I is equal to

Options

A2 9 (1+ x ^3 )^ 5 2 + 2 3 (1+ x ^3 )^ 3 2 + c
B2 9 (1+ x ^3 )^ 3 2 - 2 3 (1+ x ^3 )^ 1 2 + c
C| x + 1+x^3 |+c
Dx^2 (1+x^3 )+c

Correct answer

B. 2 9 (1+ x ^3 )^ 3 2 - 2 3 (1+ x ^3 )^ 1 2 + c

Step-by-step solution

aligned & I= x^5 d x 1+x^3 & 1+x^3=t^2 & 3 x^2 d x=2 t d t & I= 2 3 (t^2-1 ) t d t t = 2 3 (t^2-1 ) d t= 2 3 [t^3 1 3 -t ]+C & = 2 9 [t^3-3 t ]+C= 2 9 t^3- 2 3 t+C= 2 9 (1+x^3 )^ 3 / 2 - 2 3 (1+x^3 )^ 1 / 2 + C aligned

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