Question

integrate the function (x³ - 1)⅓*x^5 .dx

Answer 1

HELLO DEAR,

given function is ∫(x³ - )^⅓ x^5.dx

let (x³ - 1) = t , and x³ = (1 + t)
⇒3x² = dt/dx
⇒dx = dt/3x²

So, ∫(x³ - 1)^⅓ x^5 * dt/3x²

⇒1/3 ∫t^⅓ (1 + t) *dt

⇒1/3 ∫(t^⅓ + t^{4/3}).dt

⇒1/3 ∫t^{1/3}.dt + 1/3∫t^{4/3}.dt

⇒1/3$\bold{\frac{t^{4/3}}{4/3}}$ + 1/3$\bold{\frac{t^{7/3}}{7/3}}$ + c

put the value of t in the above function,

⇒$\bold{\frac{(x^3 - 1)^{4/3}}{4} + \frac{(x^3 - 1)^{7/3}}{7} + c}$.


I HOPE ITS HELP YOU DEAR,
THANKS