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Section 5.2 : Computing Indefinite Integrals
3. Evaluate \( \displaystyle \int{{10{t^{ - 3}} + 12{t^{ - 9}} + 4{t^3}\,dt}}\).
Show SolutionThere really isn’t too much to do other than to evaluate the integral.
\[\int{{10{t^{ - 3}} + 12{t^{ - 9}} + 4{t^3}\,dt}} = \frac{{10}}{{ - 2}}{t^{ - 2}} + \frac{{12}}{{ - 8}}{t^{ - 8}} + \frac{4}{4}{t^4} + c = \require{bbox} \bbox[2pt,border:1px solid black]{{ - 5{t^{ - 2}} - \frac{3}{2}{t^{ - 8}} + {t^4} + c}}\]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.