# Integral using Chain Rule

1. Jul 18, 2013

### better361

how do I find the integral of ∫√(t^4+x^3)dt from 0 to x^2?

2. Jul 18, 2013

### lurflurf

$$\int_0^{x^2} \! \sqrt{t^4+x^3} \, \mathop{dt}$$

unless x depends on t treat it as a constant inside the integral
find

$$\mathop{I}(a,b,C)=\int_a^{b} \! \sqrt{t^4+C} \, \mathop{dt}$$

(note this is an eliptic integral)
then

$$\int_0^{x^2} \! \sqrt{t^4+x^3} \, \mathop{dt}=\mathop{I}(0,x^2,x^3)$$