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Section 5.2 : Computing Indefinite Integrals
4. Evaluate \( \displaystyle \int{{{w^{ - 2}} + 10{w^{ - 5}} - 8\,dw}}\).
Show SolutionThere really isn’t too much to do other than to evaluate the integral.
\[\int{{{w^{ - 2}} + 10{w^{ - 5}} - 8\,dw}} = \frac{1}{{ - 1}}{w^{ - 1}} + \frac{{10}}{{ - 4}}{w^{ - 4}} - 8w + c = \require{bbox} \bbox[2pt,border:1px solid black]{{ - {w^{ - 1}} - \frac{5}{2}{w^{ - 4}} - 8w + c}}\]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.