Section 5.2 : Computing Indefinite Integrals
2. Evaluate \( \displaystyle \int{{{z^7} - 48{z^{11}} - 5{z^{16}}\,dz}}\).
Show SolutionThere really isn’t too much to do other than to evaluate the integral.
\[\int{{{z^7} - 48{z^{11}} - 5{z^{16}}\,dz}} = \frac{1}{8}{z^8} - \frac{{48}}{{12}}{z^{12}} - \frac{5}{{17}}{z^{17}} + c = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{1}{8}{z^8} - 4{z^{12}} - \frac{5}{{17}}{z^{17}} + c}}\]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.