Section 5.2 : Computing Indefinite Integrals
14. Evaluate \( \displaystyle \int{{\sin \left( x \right) + 10{{\csc }^2}\left( x \right)\,dx}}\).
Show SolutionThere really isn’t too much to do other than to evaluate the integral.
\[\int{{\sin \left( x \right) + 10{{\csc }^2}\left( x \right)\,dx}} = \require{bbox} \bbox[2pt,border:1px solid black]{{ - \cos \left( x \right) - 10\cot \left( x \right) + c}}\]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.