Homework Sourse9x2 dx ANSWER 19 ln x 9xCSolutionLet x 5 tan Substitutio
/9x2 dx ANSWER 1/9 ln | +x| = /9x+C![/9x2 dx ANSWER 1/9 ln | +x| = /9x+CSolutionLet x = 5 tan -----------> Substitution dx = 5 sec2 Integrand = sec3 / 9tan2 d = [sec /9 + cot cosec /9] d On sim](/WebImages/43/9x2-dx-answer-19-ln-x-9xcsolutionlet-x-5-tan-substitutio-1134287-1761606715-0.webp "/9x2 dx ANSWER 1/9 ln | +x| = /9x+CSolutionLet x = 5 tan -----------> Substitution dx = 5 sec2 Integrand = sec3 / 9tan2 d = [sec /9 + cot cosec /9] d On sim")
Solution
Let x = 5 tan -----------> Substitution
dx = 5 sec2
Integrand = sec3 / 9tan2 d = [sec /9 + cot cosec /9] d
On simple integration, we get
integral = [ln(sec + tan)]/9 - cosec /9 +c
= [ln((x2 + 25) + x)]/9 - (x2 +25) / 9x +C ---------> A different constant as a result of back substitution
