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

9–61. Trigonometric integrals Evaluate the following integrals.

47. ∫ (csc⁴x)/(cot²x) 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

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.