Homework Sourseindefinite integral 1sqrtx2 49 dx A 114 ln x7x7 C B 114ln 7
indefinite integral (1/(sqrt(x^2 - 49))) dx
A) (1/14) ln ((x-7)/(x+7) +C
B) (1/14)ln ((7+x)/(7-x) +C
C) ln(x+sqrt(x^2 -49)) +C
D) ln(x+sqrt(x^2+49)) + C
A) (1/14) ln ((x-7)/(x+7) +C
B) (1/14)ln ((7+x)/(7-x) +C
C) ln(x+sqrt(x^2 -49)) +C
D) ln(x+sqrt(x^2+49)) + C
Solution
OPTION C; WORK: substitute x = 7 sec(u) and dx = 7 tan(u) sec(u) du. Then sqrt(x^2-49) = sqrt(49 sec^2(u)-49) = 7 tan(u) and u = sec^(-1)(x/7): = integral sec(u) du = log(tan(u)+sec(u))+constant Substitute back for u = sec^(-1)(x/7): = log(1/7 (sqrt(x^2-49)+x))+constant Which is equivalent for restricted x values to: = log(sqrt(x^2-49)+x)+constant
