Verify the integration formulas in Exercises 37–40.
39. ∫x coth⁻¹(x)dx = ((x²-1)/2)coth⁻¹(x) + x/2 + C

Evaluate the integrals in Exercises 77–90.

90. ∫dx/((x-2)√(x²-4x+3))

Evaluate the integrals in Exercises 91–102.

96. ∫dy/((arcsin y)(1-y²))

Evaluate the integrals in Exercises 91–102.

102. ∫(from -1/3 to 1/√3)(cos(arctan 3x))/(1+9x²) dx

Verify the integration formulas in Exercises 37–40.

37. a. ∫sech(x)dx = tan⁻¹(sinh x) + C

Find the limits in Exercises 1–6.

1. lim(b→1⁻) ∫(from 0 to b) dx/√(1-x²)

Using different substitutions

Show that the integral

∫((x² - 1)(x + 1))^(-2/3) dx

can be evaluated with any of the following substitutions.

c. u = arctan x

What is the value of the integral?

Evaluate the integral.

${\int }_{}^{}(\frac{2}{\sqrt{1-x^2}}-\frac{1}{3\sqrt{x}})dx$

Evaluate the integral.

${\int }_{\sqrt{2}}^2\frac{1}{\mid x\mid \sqrt{x^2-1}}dx$