Evaluate: $\int 2x(x^2 + 1)^4 \, dx$

Evaluate: $\int \sin^4 x \cos x \, dx$

Evaluate the cyclic integral: $\int e^x \sin x \, dx$

Evaluate: $\int x e^x \, dx$

Evaluate the integral using the Tabular Method: $\int x^3 e^{2x} \, dx$

Evaluate: $\int \sin^3 x \, dx$

Evaluate: $\int \tan^3 x \sec^4 x \, dx$

Evaluate: $\int \frac{1}{x^2 \sqrt{4 - x^2}} \, dx$

Evaluate: $\int \frac{1}{x^2 - 1} \, dx$

Evaluate: $\int \frac{2x^2 - x + 4}{x^3 + 4x} \, dx$

Evaluate the definite integral using Wallis' Formula: $\int_0^{\pi/2} \sin^6 x \, dx$