Evaluate the integrals in Exercises 41–60.
41. ∫sinh(2x)dx

Explain why or why not. Determine whether the following statements are true and give an explanation or counterexample.

d. ∫2 sin x cos x dx = −(1/2) cos 2x + C.

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. Assume ƒ, ƒ', and ƒ'' are continuous functions for all real numbers.                                                                                                                                                           

(c) ∫ sin 2𝓍 d𝓍 = 2 ∫ sin 𝓍 d𝓍 .

Evaluate the integrals in Exercises 39–56.

49. ∫3sec²t/(6 + 3tan(t)) dt

Evaluate the integrals in Exercises 39–56.

56. ∫sec(x)dx/√(ln(sec(x)+tan(x)))

Evaluate the integrals in Exercises 41–60.

43. ∫6cosh(x/2 - ln3)dx

Evaluate the integrals in Exercises 41–60.

45. ∫tanh(x/7)dx

Evaluate the integrals in Exercises 41–60.

47. ∫sech²(x - 1/2)dx

Evaluate the integrals in Exercises 41–60.

49. ∫(sech(√t)tanh(√t)dt)/√t