Question 826773
{{{y=int(12x(x^2+3)^5, dx)}}}
Let u = {{{x^2+3}}}
Then du = 2x*dx
{{{y=int(6*2x(x^2+3)^5, dx)}}}
{{{y=6*int(u^5, du)}}}
{{{y=6*(u^6/6) + C}}}
{{{y=(x^2+3)^6 + C}}}<br>
Now we'll substitute in the coordinates of the given point:
{{{7=(5^2+3)^6 + C}}}
{{{7=(25+3)^6 + C}}}
{{{7=(28)^6 + C}}}
{{{7=(28)^6 + C}}}
{{{7 = 481890304 + C}}}
{{{-481890293 = C}}}<br>
P.S. Did the brackets, [], around the coordinates mean something?
P.P.S. Going from
{{{y=6*int(u^5, du)}}}
to
{{{y=6*(u^6/6) + C}}}
is not quite correct. It should be
{{{y=6*int(u^5, du)}}}
{{{y=6*(u^6/6 + C)}}}
followed by
{{{y=6*(u^6/6) + 6C}}}
But 6C is a constant, just like C is. It is common practice to ignore the 6 and just use C. But it is possible that your teacher might want you to use the 6. In this case it is 6C which is -481890293. Divide by 6 to get the original C.