Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 2 sec^2(t)/tan^2(t) + 14 tan(t) + 48 dt

Complete the square in the denominator to get

tan²(t ) + 14 tan(t ) + 48 = tan²(t ) + 14 tan(t ) + 49 - 1

… = (tan(t ) + 7)² - 1

Substitute u = tan(t ) + 7 and du = sec²(t ) dt. Then the integral becomes

Separate the integrand into partial fractions:

Then we get

29 mil

step-by-step explanation: