7. Antiderivatives & Indefinite Integrals

Evaluate the integral: ${\int }_1^7{w}^2\ln \left(w\right) dw$

Evaluate the double integral by reversing the order of integration: ${\int }_0^4{\int }_{3y}^{12}13e^{x^2} dx dy$

Evaluate the integral: ${\int }_0^{\frac{\pi }{2}}3{\cos }^2\left(x\right) dx$.

Evaluate the integral. (Use c for the constant of integration.) $\int 4{\sin }^2\left(x\right){\cos }^3\left(x\right)dx$

Evaluate the integral: ${\int }_0^{\pi }x\sin \left(x\right)\cos \left(x\right)dx$

Evaluate the integral: ${\int }_{}^{}\arctan \left(\frac{1}{x}\right)dx$

4. What substitutions are made to evaluate integrals of sin(mx)sin(nx), sin(mx)cos(nx), and cos(mx)cos(nx)? Give an example of each case.

9–61. Trigonometric integrals Evaluate the following integrals.

47. ∫ (csc⁴x)/(cot²x) dx

Evaluate the integrals in Exercises 31–56. Some integrals do not require integration by parts.

∫ sin(2x) cos(4x) dx

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

$g\(\left\)(\(\theta\[\right\))=\(\int\)^{}\(\left\)(5\(\sec\)^2\(\theta\)-2\(\csc\)^2\(\theta\]\right\))d\(\theta\)$

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