111 Section 5.7 Inverse Trigonometric Functions: Integration Section 5.7 Inverse Trigonometric Functions: Integration Course Number Objective: In this lesson you learned how to find antiderivatives of Instructor inverse trigonometric functions. Date Integrals Involving Inverse Trigonometric Functions What you should learn (Pages How to integrate functions whose Let be a differentiable function of and let > 0. u x, a antiderivatives involve inverse trigonometric functions du a2 u2 = arcsin (u/a) + . C du + = (1/a) arctan (u/a) + . a2 u2 C = (1/a) arcsec (| | /a) + . u C du u u2 a2 6x dx 4 9x4 + Example 1: ½ arctan(3x2/2) + C Example 3: Complete Completing the Square (Pages the square for the Completing the square helps when quadratic functions are involved in the integrand . 2x2 + 16x . Example 2: Complete the square for the polynomial: 2[(x + 4)2 16] 6x 3 . + + x2 (x + 3)2 6 What you should How to use the method of completing the square to integrate a function
Section 5.7 Inverse Trigonometric Functions: Integration 111 Section 5.7 Inverse Trigonometric Functions: Integration Objective: In this lesson you learned how to find antiderivatives of inverse trigonometric functions. Course Number Instructor Date Integrals Involving Inverse Trigonometric Functions (Pages Let u be a differentiable function of x, and let a > 0. du What you should learn How to integrate functions whose antiderivatives involve inverse trigonometric functions a2 u2 = arcsin (u/a) + C . du a2 + u2 = (1/a) arctan (u/a) + C . du u u2 a2 Example 1: = (1/a) arcsec (| u | /a) + C . 6x dx 4 + 9x4 ½ arctan(3x2/2) + C Completing the Square (Pages Completing the square helps when quadratic functions are involved in the integrand . Example 2: Complete the square for the polynomial: x2 + 6x + 3 . (x + 3)2 6 Example 3: Complete the square for the 2x2 + 16x . 2[(x + 4)2 16] What you should How to use the method of completing the square to integrate a function
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