Evaluate the integrals in Exercises 87–96.
95. ∫₂⁴ x^(2x) (1 + ln x) dx

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

35. y = ln((x²+1)^5/√(1-x))

Evaluate the integrals in Exercises 87–96.

87. ∫ 5ˣ dx

Evaluate the integrals in Exercises 39–56.

43. ∫(from 0 to π)(sin t)/(2 - cos t) dt

Use l’Hôpital’s rule to find the limits in Exercises 7–52.

35. lim (x → 0⁺) ln(x² + 2x) / ln x

137. Find a curve through the origin in the xy-plane whose length from x = 0 to x = 1 is L = ∫ from 0 to 1 of sqrt(1 + (1/4)e^x) dx.

Use l’Hôpital’s rule to find the limits in Exercises 7–52.

7. lim (x → 2) (x - 2) / (x² - 4)