Consider the indefinite integral sec(r) + sec(r) tan(r) dr. sec(r) + tan(z) Evaluate this integral using...

 

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Consider the indefinite integral sec²(r) + sec(r) tan(r) dr. sec(r) + tan(z) Evaluate this integral using the substitution u = sec(x) + tan(x). (b) Simplify the original integrand in part (a) by factoring the numerator. What is a simpler way to write the integrand? (c) Combine your work in (a) and (b) to compute sec(z) dr. (d) Using parts (a)-(c) as a guide, evaluate esc(z) dr Consider the indefinite integral sec²(r) + sec(r) tan(r) dr. sec(r) + tan(z) Evaluate this integral using the substitution u = sec(x) + tan(x). (b) Simplify the original integrand in part (a) by factoring the numerator. What is a simpler way to write the integrand? (c) Combine your work in (a) and (b) to compute sec(z) dr. (d) Using parts (a)-(c) as a guide, evaluate esc(z) dr