11. Integrals of Inverse, Exponential, & Logarithmic Functions

Evaluate the integrals in Exercises 33–54.

∫(from ln4 to ln9)e^(x/2)dx

Evaluate the integrals in Exercises 33–54.

∫ 2t e^(-t²) dt

Evaluate the integrals in Exercises 31–78.

55. ∫(from -2 to -1)e^(-(x+1)) dx

Evaluate the integrals in Exercises 31–78.

31. ∫e^x sin(e^x)dx

Evaluate the integrals in Exercises 31–78.

49. ∫x3^(x²)dx

Find the definite integral.

${\int }_{-1}^1{x}^2{e}^{x^3}dx$

Evaluate the integrals in Exercises 31–78.

33. ∫e^x sec²(e^x - 7)dx

2–9. Integrals Evaluate the following integrals.

∫₁⁴ (10^{√x} / √x) dx

Oil consumption Starting in 2018 (t=0), the rate at which oil is consumed by a small country increases at a rate of 1.5%/yr, starting with an initial rate of 1.2 million barrels/yr.

b. Find the function that gives the amount of oil consumed between t=0 and any future time t.

Evaluate the integrals in Exercises 33–54.

∫8e^(x+1) dx

Evaluate the indefinite integral. 

${\int }_{}^{}-{\left(6\right)}^{x}dx$

What is the indefinite integral of $e^{5x}$ with respect to $x$?

Evaluate the indefinite integral.

${\int }_{}^{}{e}^{\sec \theta }\sec \theta \tan \theta d\theta$

Evaluate the integrals in Exercises 33–54.

49. ∫ e^(sec πt) sec πt tan πt dt

Evaluate the indefinite integral.

${\int }_{}^{}2{\left(\frac{1}{3}\right)}^{x}dx$