11. Integrals of Inverse, Exponential, & Logarithmic Functions

The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.

∫ (2^(√y) dy) / 2√y

Evaluate the integrals in Exercises 87–96.

89. ∫₀¹ 2^(−θ) dθ

Evaluate the integrals in Exercises 87–96.

91. ∫₁^(√2) x·2^(x²) dx

Evaluate the integrals in Exercises 87–96.

93. ∫₀^(π/2) 7^(cos t) sin t dt

Evaluate the integrals in Exercises 31–78.

49. ∫x3^(x²)dx

Evaluate the integrals in Exercises 31–78.

35. ∫sec²x e^(tan x)dx

Evaluate the integrals in Exercises 33–54.

∫ 2t e^(-t²) dt

Evaluate the integrals in Exercises 33–54.

∫ (e^(1/x) / x²) dx

Evaluate the integrals in Exercises 33–54.

49. ∫ e^(sec πt) sec πt tan πt dt

Evaluate the integrals in Exercises 33–54.

51. ∫ from ln(π/6) to ln(π/2) 2e^v cos(e^v) dv

Evaluate the integrals in Exercises 33–54.

53. ∫ (e^r / (1 + e^r)) dr

Evaluate the integrals in Exercises 31–78.

31. ∫e^x sin(e^x)dx

Evaluate the integrals in Exercises 31–78.

33. ∫e^x sec²(e^x - 7)dx

Evaluate the integrals in Exercises 33–54.

∫(e^(3x) + 5e^(-x)) dx

Evaluate the integrals in Exercises 33–54.

∫8e^(x+1) dx