Most Important Selected Qs for JEE AdvancedMathematicsIndefinite Integration

If f(x) d x= (x) , then x^5 f (x^3 ) d x is equal to:

Options

A1 3 x^3 (x^3 )- x^2 (x^3 ) d x+C
B1 3 [x^3 (x^3 )- x^3 (x^3 ) d x ]+C
C1 3 [x^3 (x^3 )- x^2 (x^3 ) d x ]+C
D1 3 x^3 (x^3 )-3 x^3 (x^3 ) d x+C

Correct answer

A. 1 3 x^3 (x^3 )- x^2 (x^3 ) d x+C

Step-by-step solution

By Newton & libnitz rule f(x)= ^ (x) aligned & Put x^3=t d t d x =3 x^2 & = 1 3 t f(t) d t= 1 3 t ^ (t) d t= 1 3 [t (t)- (t) d t ] & = 1 3 x^3 (x^3 )- x^2 (x^3 ) d x aligned

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