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6:04In Exercises 35–68, use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integrals for convergence. If more than one method applies, use whatever method you prefer.
∫ from 2 to ∞ of ((x dx) / √(x⁴ - 1))
In Exercises 39–48, use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.
∫ (e^{t} dt) / ((1 + e^{2t})^{3/2}) from ln(3/4) to ln(4/3)
Use reduction formulas to evaluate the integrals in Exercises 41–50.
∫ 8 cot^4(t) dt
In Exercises 9–16, express the integrand as a sum of partial fractions and evaluate the integrals.
∫ (y + 4) / (y² + y) dy from 1/2 to 1
Use any method to evaluate the integrals in Exercises 15–38. Most will require trigonometric substitutions, but some can be evaluated by other methods.
∫ (x² dx) / (4 + x²)
Use any method to evaluate the integrals in Exercises 15–38. Most will require trigonometric substitutions, but some can be evaluated by other methods.
∫ dx / √(1 - x²)
