Integration question

[old shore]

how can i continue with this?

[hazy drum]

idt there's an elementary antiderivative

you're gonna need to calculate it numerically

[old shore]

can i do it like this?

[restive comet]

you evaluated the terms under the radical separately which is incorrect.

that's like saying sqrt(4 + 1) = 2 + 1

so I was able to solve for the (-2y^2)sqrt(y^3 + 1) part

but I honestly have no idea how to do just the 2sqrt(y^3 + 1) part

sqrt(y^2 + 1) is already a pretty complicated antiderivative

so y^3 is a bit above my current level of expertise

for the part I was able to solve though

use a u-sub of u^2 = y^3 + 1

Ok after trying an antiderivative calculator I believe there is no elementary solution

though that's just for the general antiderivative