first the second term can be split up to make integrating it easierits easier if the x^{3 }component is separatedthis eventually simplifies the second term to (-1/4) * x^{-3}so now the question is integrate (2x^{5} - (1/4)*x ^{-3} -5) dx. For the first term, when integrating, the x term increases by 1 power and then the coefficient of x is divided by that new power thus the first term becomes 1/3 x^{6}. The second term, repeat the same steps as before, while watching out for multiplying minus signs.this means the integrated form of the second term is 1/8*x