Question

solve the question of integration class 11th

Answer 1

I = (x +1)(x -2).dx/x⅓

Let x⅓ = z
take cube both sides,
x = z³
differentiate wrt x
dx = 3z².dz

I = (z³ + 1)(z³ -2)3z².dz/z
= (z³ + 1)(z³ -2).3z.dz
= (z^6 -z³ -2)3z.dz
= (3z^7 - 3z⁴ -6z)dz
= 3z^7.dz -3z⁴.dz - 6z.dz
= 3z^8/8 -3z^5/5 -3z² + C
put z = x⅓

I = (3/8).x^8/3 -(3/5)x^5/3 -3x⅔ + C