11. Integrals of Inverse, Exponential, & Logarithmic Functions

37–56. Integrals Evaluate each integral.

∫₀ ˡⁿ ² tanh x dx

2–9. Integrals Evaluate the following integrals.

∫ dx / √(x² − 9),x > 3

Find the indefinite integral.

${\int }_{}^{}\frac{-2}{x^2-12x+45}dx$

Evaluate the integrals in Exercises 91–102.

99. ∫1/(√x (x+1)((arctan√x)²+9)) dx

Evaluate the integrals in Exercises 1–14.

∫ (2 dx) / (x³ √(x² - 1)), where x > 1

Find the indefinite integral.

${\int }_{}^{}\frac{se{c}^2\left(si{n}^{-1}\theta \right)}{\sqrt{1-{\theta }^2}}d\theta$

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.

∫ tan^(-1)(x) / x² dx

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.

∫ (x² / (x² + 1)) dx

Evaluate the integrals in Exercises 31–78.

73. ∫dx/√(-2x-x²)

Evaluate the integrals in Exercises 1–14.

∫ (2 dx) / √(1 - 4x²) from 0 to 1/(2√2)

In Exercises 27–40, use a substitution to change the integral into one you can find in the table. Then evaluate the integral.

∫ cos^(-1)(√x) / √x dx

Use Table 5.6 to evaluate the following definite integrals.                                                                                                                    

 (c) ∫₃√₂^⁶ d𝓍/(𝓍² ―9)

Evaluate the integrals in Exercises 53–76.

67. ∫dx/(2+(x-1)²)

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.

∫ x arctan(x) dx

61–62. Points of intersection and area

b. Compute the area of the region described.

f(x) = sinh x, g(x) = tanh x; the region bounded by the graphs of f, g, and x = ln 3