Calculus 1: U Substitution

Use U-Substitution to evaluate the following integral

$\displaystyle\int 4x(x^2 + 5)^{50} \ dx$

Evaluate the following integral

$\displaystyle\int\cos^4(x)\sin(x) \ dx$

Evaluate the following integral

$\displaystyle\int (x + 1) \sqrt{2x + x^2} \ dx$

Evaluate the following integral

$\displaystyle\int\frac{\sin (\ln (x))}{x} \ dx$

Evaluate the following integral

$\displaystyle\int x^3 \sin (x^4 + 2) \ dx$

Find $\displaystyle\int\sin(x)\sin(\cos{x}) \ dx$

Evaluate $\displaystyle\int x^5 \sqrt{1 + x^2} \ dx$

Evaluate the indefinite integral

$\displaystyle\int (x^4 + 2)^4 4x^3 \ dx$

Find $\displaystyle\int\frac{2x}{1 + 2x^2} \ dx$

Evaluate $\displaystyle\int (\ln{x})^4 \frac{2}{x} \ dx$

Evaluate $\displaystyle\int\frac{e^{ \ p \ \tan^{-1}(x)}}{1 + x^2} \ dx$