If the integral I=∫(x^5)/(√(1+x^3))dx =K√(x^3+1)x^3-2+C, (where, C is the constant of integration), then the value of 9K is equal to

Question

MARKS Content Team · Accepted Answer

Correct answer: (B) 2. Let 1+x^3=t^2 ⇒3x^2dx=2tdt ⇒I=∫(t^2-12t dt)/3t ⇒I=2/3∫t^2-1dt =(2t^3)/9-2/3t+C =2/9tt^2-3+C =2/9√(1+x^3)x^3-2+C ∴K=2/9⇒9K=2

If the integral $I = \int \frac{x^{5}}{\sqrt{1 + x^{3}}} d x$ $= K \sqrt{x^{3} + 1} (x^{3} - 2) + C,$ (where, $C$ is the constant of integration), then the value of $9 K$ is equal to