Example 2: Evaluate the inverse trig integral ∫ sec-1x dx. Solution: By using integration by parts: ∫ sec-1x· 1 dx = sec-1x∫ dx - ∫ [d/dx (sec-1x) ∫ 1 dx] dx = sec-1x (x) - ∫ ( 1/(x√x²-1)) x dx = x sec-1x - ∫ (1 / √√(x²-1)) dx Su...
Inverse Trig FunctionDerivativeIntegral arcsin x 1/√1-x² x arcsin x + √1-x² + C arccos x -1/√1-x² x arccos x - √1-x² + C arctan x 1/(1+x²) x arctan x - (1/2) ln |x2+1| + C arccsc x -1/(|x|√x²-1) x arccsc x + ln |x + √x²...
Advice tothe reader: The methods in this section aren’t really very useful in trigonometry itself, but are used in integral calculus and some physics or engineering courses. You may wish to skip them, especially on a first reading. On the other hand, they are pretty cool....