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Problem 8.PE.129
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
129. ∫ (x^(ln x) * ln x) / x dx
Problem 8.PE.97
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
∫ θ·cos(2θ + 1) dθ
Problem 8.PE.4
Evaluate the integrals in Exercises 1–8 using integration by parts.
∫ arccos(x / 2) dx
Problem 8.PE.42
Evaluate the integrals in Exercises 37–44.
∫ sec²(θ) sin³(θ) dθ
Problem 8.PE.105
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
∫ (z + 1) / [z²(z² + 4)] dz
Problem 8.PE.87
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
∫ cotx·csc³x dx
Problem 8.PE.93
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
∫ (2 − cosx + sinx) / sin²x dx
Problem 8.PE.123
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
123. ∫ √x * √(1 + √x) dx
Problem 8.PE.107
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
∫ t dt / √(9 − 4t²)
Problem 8.PE.77
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
∫₋₁⁰ e^x / (e^x + e^(−x)) dx
Problem 8.PE.48
You are planning to use Simpson’s Rule to estimate the value of the integral Estimate ∫ from 1 to 2 of f(x) dx with an error magnitude less than 10⁻⁵ using Simpson’s Rule.
You have determined that |f⁽⁴⁾(x)| ≤ 3 throughout the interval of integration. How many subintervals should you use to ensure the required accuracy?
(Remember that for Simpson’s Rule the number of subintervals must be even.)
Problem 8.PE.10
Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.
∫ [x / (x² + 4x + 3)] dx
Problem 8.PE.57
Evaluate the improper integrals in Exercises 53–62.
∫ from 3 to ∞ of (2 / (u² − 2u)) du
Problem 8.PE.117
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
117. ∫ dr / (1 + √r)
Problem 8.PE.61
Evaluate the improper integrals in Exercises 53–62.
∫ from −∞ to ∞ of (1 / (4x² + 9)) dx
Problem 8.PE.109
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
∫ e^t dt / (e^(2t) + 3e^t + 2)
Problem 8.PE.22
Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.
∫ [(x³ + 1) / (x³ − x)] dx
Problem 8.PE.115
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
∫ (sin5t) dt / [1 + (cos5t)²]
Problem 8.PE.14
Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.
∫ [cos(θ) / (sin²(θ) + sin(θ) − 6)] dθ
Problem 8.PE.125
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
125. ∫ dx / (√x * √(1 + x))
Problem 8.PE.59
Evaluate the improper integrals in Exercises 53–62.
∫ from 0 to ∞ of (x² * e^(−x)) dx
Problem 8.PE.6
Evaluate the integrals in Exercises 1–8 using integration by parts.
∫ x² sin(1 − x) dx
Problem 8.PE.20
Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.
∫ [t / (t⁴ − t² − 2)] dt
Problem 8.PE.91
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
∫ √(2x − x²) dx
Problem 8.PE.28
Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.
∫ [1 / √(e^s + 1)] ds
Problem 8.PE.95
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
∫ 9 dv / (81 − v⁴)
Problem 8.PE.29b
Evaluate the integrals in Exercises 29–32 (b) using a trigonometric substitution.
∫ [y / √(16 − y²)] dy
Problem 8.PE.24
Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.
∫ [(2x³ + x² − 21x + 24) / (x² + 2x − 8)] dx
Problem 8.PE.133
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
133. ∫ (sin²x) / (1 + sin²x) dx
Problem 8.PE.111
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
∫₁^∞ (lny) / y³ dy