Question

evaluate the integral from -1 to 0 of (2x^5+6x)^3(5x^4+3)dx using substitution and the antiderivative

Answer 1

let \( u = (2x^5 +6x) \) and \( du = (10x^4+6) \ dx\)
solving for dx we get
\[ dx = \frac{du}{2(5x^4+3) } \]
the lower limit x= -1 corresponds to u= -2-6= -8
the upper limit x=0 corresponds to u=0
substitute into your problem to get
\[ \frac{1}{2} \int_{-8}^0 u^3 du\]