Once we’ve gotten the root converted to a fractional exponent and the \(y\)’s out of the denominator there really isn’t too much to do other than to evaluate the integral.

\[\begin{align*}\int{{\frac{7}{{3{y^6}}} + \frac{1}{{{y^{10}}}} - \frac{2}{{\sqrt[3]{{{y^4}}}}}\,dy}} & = \int{{\frac{7}{3}{y^{ - 6}} + {y^{ - 10}} - 2{y^{ - \,\frac{4}{3}}}\,dy}}\\ & = \frac{7}{3}\left( {\frac{1}{{ - 5}}} \right){y^{ - 5}} + \left( {\frac{1}{{ - 9}}} \right){y^{ - 9}} - 2\left( { - \frac{3}{1}} \right){y^{ - \,\frac{1}{3}}} + c\\ & = \require{bbox} \bbox[2pt,border:1px solid black]{{ - \frac{7}{{15}}{y^{ - 5}} - \frac{1}{9}{y^{ - 9}} + 6{y^{ - \,\frac{1}{3}}} + c}}\end{align*}\]

Don’t forget to add on the “+c” since we know that we are asking what function did we differentiate to get the integrand and the derivative of a constant is zero and so we do need to add that onto the answer.