2. Evaluate the following definite integrals using u-substitution. X a. Jo (1+x2)3 dx re sin(In x) b. 1 dx X C. J_RI/2 cos(x) sin(x) dx7. This problem centers on finding antiderivatives for the basic trigonometric functions other than sin(a) and cos(a). a. Consider the indefinite integral Stan(x) dx. By rewriting the integrand as tan(x) = sin(x) cos(a) and identifying an appropriate function-derivative pair, make a u-substitution and hence evaluate f tan(x) dac. b. In a similar way, evaluate f cot(x) da. c. Consider the indefinite integral sec2 (a) + sec(a) tan(a) dx. sec(x) + tan(x) Evaluate this integral using the substitution u = sec(x) + tan(x). d. Simplify the integrand in (c) by factoring the numerator. What is a far simpler way to write the integrand? e. Combine your work in (c) and (d) to determine f sec(x) dx. f. Using (c)-(e) as a guide, evaluate S csc(x) dac