Question 1029789
{{{int(((4x^6+2x)^3(12x^5+1)),dx,-1,0)}}}
Let {{{u=4x^6+2x}}},
{{{du=(24x^5+2)dx}}}
{{{du/2=(12x^5+1)dx}}}
Check the limits, when {{{x=0}}}, {{{u=0}}}
When {{{x=-1}}}, {{{u=4-2=2}}}
Substituting,
{{{int(((4x^6+2x)^3(12x^5+1)),dx,-1,0)=int((1/2)u^3,du,x=2,0)}}}
{{{int(((4x^6+2x)^3(12x^5+1)),dx,-1,0)=-int((1/2)u^3,du,x=0,2)}}}
{{{int(((4x^6+2x)^3(12x^5+1)),dx,-1,0)=-u^4/8+C}}}
{{{int(((4x^6+2x)^3(12x^5+1)),dx,-1,0)=-2^4/8}}}
{{{int(((4x^6+2x)^3(12x^5+1)),dx,-1,0)=-16/8}}}
{{{highlight(int(((4x^6+2x)^3(12x^5+1)),dx,-1,0)=-2)}}}