Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.
Section 5.2 : Computing Indefinite Integrals
21. Evaluate \( \displaystyle \int{{6\cos \left( z \right) + \frac{4}{{\sqrt {1 - {z^2}} }}\,dz}}\).
Show SolutionThere really isn’t too much to do other than to evaluate the integral.
\[\int{{6\cos \left( z \right) + \frac{4}{{\sqrt {1 - {z^2}} }}\,dz}} = \require{bbox} \bbox[2pt,border:1px solid black]{{6\sin \left( z \right) + 4{{\sin }^{ - 1}}\left( z \right) + c}}\]Note that because of the similarity of the derivative of inverse sine and inverse cosine an alternate answer is,
\[\int{{6\cos \left( z \right) + \frac{4}{{\sqrt {1 - {z^2}} }}\,dz}} = \require{bbox} \bbox[2pt,border:1px solid black]{{6\sin \left( z \right) - 4{{\cos }^{ - 1}}\left( z \right) + c}}\]