7. Antiderivatives & Indefinite Integrals

Find $g\(\left\)(x\(\right\))$ by evaluating the following indefinite integral.

$g\(\left\)(x\(\right\))=\(\int\]\left\)(\(\sin\)^2x-100\(\csc\) x\(\cot\) x+\(\cos\)^2x\(\right\))dx$

Evaluating integrals Evaluate the following integrals.                                                                                                                                      

 ∫ 𝓍² cos 𝓍³ d𝓍

Evaluating integrals Evaluate the following integrals.                                                                                                                                         

 ∫ (cos 7ω) /(16 + sin² 7ω) dω 

Evaluating integrals Evaluate the following integrals.                                                                                                                                         

 ∫(√1 + tan 2t) sec² 2t dt

Evaluating integrals Evaluate the following integrals.                                                                                                                                         

 ∫ sin 𝒵 sin (cos 𝒵) d𝒵

Evaluating integrals Evaluate the following integrals.                                                                                                                                         

 ∫ 𝓍 sin 𝓍² cos⁸ 𝓍² d𝓍

68. Different methods

a. Evaluate ∫(cot x csc² x) dx using the substitution u=cotx.

69. Different substitutions

b. Evaluate ∫(tan x sec² x) dx using the substitution u=secx.

7–64. Integration review Evaluate the following integrals.

53. ∫ eˣ sec(eˣ + 1) dx

3. Describe the method used to integrate sin³x.

4. Describe the method used to integrate sinᵐx cosⁿx, for m even and n odd.

5. What is a reduction formula?

7. How would you evaluate ∫ tan¹⁰x sec²x dx?

9–61. Trigonometric integrals Evaluate the following integrals.

31. ∫ 20 tan⁶x dx

9–61. Trigonometric integrals Evaluate the following integrals.

32. ∫ cot⁵(3x) dx