Question

Н НС Cam Н НС Can Can Can Н НЕС wLog Mas how wUna Can New Can Cen C https//www.webassign.net/wcb/Student/Assignment Responscs/last?dcp-21260896a1 Need Help? Talk to a Tutor Read It Master It 1 points LarCalc11 5.9.075.MI. 13. My Notes Find the indefinite integral using the formulas from the theorem regarding differentiation and integration involving inverse hyperbolic functions. (Use C for the constant of integration. Remember to use absolute values where appropriate.) dx 6 36x2 Need Help? Talk to a Tutor Read It Watch It Master It -1 points LarCalc11 5.9.080. My Notes 14. Find the indefinite integral using the formulas from the theorem regarding differentiation and integration involving inverse hyperbolic functions. (Use C for the constant of integration.) 11:36 PM ENG E/01/2015 Type here to search 2

Answer 1

Problem: 1 da 6 362 Apply linearity: 1 1 da 6a21 6 Now solving: 1 da 6a2-1 Factor the denominator: - / da 6x 6 6a + Perform partial fraction decomposition: 3 3 da V6 ( 62 6 ( 6x 6 _ Apply linearity: 3 1 3 1 da 6 6 dr 6x -6 Now solving: 1 da 6x -6 Substitute u 6x - /6- dæ du (steps) 6 1 du 6

Now solving: du u This is a standard integral: In(u) Plug in solved integrals: 1 1 du 6 In(u) 6 6a-6 Undo substitution u In 6x 6 Now solving: 1 da 6x 6 Substitute u 6x + /6> dæ du (steps) 6 1 du 6 Use previous result: In(u) 6 6x 6 Undo substitution u In6x 6

Plug in solved integrals 3 1 3 1 da da V6 V6 6x 3 ln 6x 3 ln 6x 6 3 6 Plug in solved integrals: 1 1 da 6x2 1 6 In 6 6 In 6x 6 3 3 2-6 2-6 The problem is solved. Apply the absolute value function to arguments of logarithm functions in order to extend the antiderivative's domain: 1 da 6 36x2 In(6x v6 In 6a 6 C 3 3 2.6 2-6 Rewrite/simplify (6r+ vGl) (ie n 6r n 6a 6 C 3 2-6