Compute the value of $$\int_0^2\sqrt{\frac{4-x}{x}}-\sqrt{\frac{x}{4-x}}dx$$

Find the derivative of $x^x$.

Compute the value of $$\lim_{x\to\pi}\frac{\ln(2+\cos{x})}{\left(3^{\sin{x}}-1\right)^2}$$

Compute the value of $$\lim_{n\to\infty}n^2\left(1-\cos\frac{\pi}{n}\right)$$

Let $$f(x)=\left\{\begin{array}{ll} \cos{x} &, x\in[-\frac{\pi}{2}, 0)\\e^x&,x\in[0,1] \end{array}\right.$$

Compute $\displaystyle\int_{-\frac{\pi}{2}}^{1}f(x)dx$.

Determine whether or not these two series converge: $$(A)\ \ \sum_{n=1}^{\infty}\sin\left(\frac{\cos{n}}{n^2}\right)\qquad (B)\ \  \sum_{n=1}^{\infty}\cos\left(\frac{\sin{n}}{n^2}\right)$$

The equation $x^y=y^x$ describes a curve in the first quadrant of the plane containing the point $P=(4, 2)$. Compute the slope of the line that is tangent to this curve at $P$.

Compute $$\int\frac{1}{\sin{x}}d{x}$$

Compute $$\int_0^{\frac{\pi}{4}}\frac{1}{\sin{x}+\cos{x}}d{x}$$

If water is poured into a right cone whose height is $H$ cm and base's radius is $R$ cm at a speed of $A$ $cm^3$ per second, what is the speed the water is rising when the depth of water is half of the cone's height?

Let $f(x)=x^2\cos(ax)$ where $a$ is a constant. Find the $50^{th}$ order derivative of $f(x)$, i.e. $f^{(50)}(x)$.

The three segments marked with lengths are perpendicular to each other. Find the area of the outside square.

Compute $$\int\sin^5{x}dx$$

Compute $$\int\sec{x}dx$$

Compute $$\int\sec{x}dx$$

Compute $$\int\frac{1}{\sqrt{x^2+1}}dx$$

Compute $$\int\frac{1}{\sqrt{x^2+4x+5}}dx$$

Compute $$\int x^3\ln{x}d{x}$$

Compute $$\int\arctan{x}dx$$

Evaluate $$\int e^{ax}\cos(bx)d{x}\quad\text{and}\quad\int e^{ax}\sin(bx)d{x}$$

Evaluate $$\int x^2e^xd{x}$$

Evaluate $$\int x^2\sin{x}dx$$

Evaluate $$\int\frac{1}{\sqrt{x^2 + a^2}}dx$$

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