Integrals giving inverse trig functions practice problems
Integrals that land on arctan and arcsin, including completing the square. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
Evaluate \( \displaystyle \int \frac{1}{x^{2} + 16}\, dx \).
Evaluate \( \displaystyle \int_{0}^{\sqrt{3}} \frac{1}{\sqrt{4 - x^{2}}}\, dx \).
Evaluate \( \displaystyle \int \frac{4}{x^{2} + 25}\, dx \).
Evaluate \( \displaystyle \int \frac{3}{\sqrt{4 - x^{2}}}\, dx \).
Evaluate \( \displaystyle \int_{0}^{2 \sqrt{3}} \frac{3}{x^{2} + 4}\, dx \).
Evaluate \( \displaystyle \int_{0}^{4} \frac{2}{x^{2} + 16}\, dx \).
Evaluate \( \displaystyle \int_{0}^{2} \frac{4}{\sqrt{- x^{2} + 2 x + 3}}\, dx \).
Evaluate \( \displaystyle \int \frac{4}{\sqrt{- x^{2} - 6 x}}\, dx \).
Evaluate \( \displaystyle \int \frac{2}{x^{2} - 6 x + 10}\, dx \).
Evaluate \( \displaystyle \int \frac{2}{x^{2} + 4 x + 13}\, dx \).