Let's integrate 2

Calculus Level 2

$\displaystyle \int \dfrac{x^3}{\sqrt[3]{1+x^4}} dx$

If the value of above expression is in the form $\frac{A}{B}\sqrt[X]{(1+x^4)^{Y}}+C$ , where $A,B,X,Y$ are positive integers with $\gcd(A,B) = \gcd(X,Y) = 1$ , find $A+B+X+Y$ .

The answer is 16.

1 solution

Harsh Khatri
Feb 14, 2016

Substituting $x^4+1 = t$ ,

$\displaystyle \frac{1}{4} \int t^{\frac{-1}{3}} dt$

$\displaystyle \Rightarrow \frac{3}{8} t^{\frac{2}{3} } +C$

$\displaystyle \Rightarrow A+B+X+Y = 3 + 8 + 3 + 2 = \boxed{16}$

Let's integrate 2

The answer is 16.

1 solution

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