Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
d. ∫(1/eˣ) dx = ln eˣ + C.

60–69. Completing the square Evaluate the following integrals.

68. ∫ dx / sqrt((x - 1)(3 - x))

Variations on the substitution method Evaluate the following integrals.                                                                                                        

 ∫ 𝓍/(∛𝓍 + 4) d𝓍

Multiple substitutions If necessary, use two or more substitutions to find the following integrals.                                                                                    

  ∫ d𝓍 / [√1 + √(1 + 𝓍)] (Hint: Begin with u = √(1 + 𝓍 .)  

7-56. Trigonometric substitutions Evaluate the following integrals using trigonometric substitution.

16. ∫ x²/(25 + x²)² dx

Indefinite integrals Use a change of variables or Table 5.6 to evaluate the following indefinite integrals. Check your work by differentiating.                                                                                  

 ∫ sin 𝓍 sec⁸ 𝓍 d𝓍

Find the following indefinite integral.

$\int-300dx$

Find the following indefinite integral.

$\int4x^3dx$

Find the following indefinite integral.

$\int 100x^{99}dx$