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. $f^{(50)}(x)$.

Estimate the value of $\sqrt[4]{10018}$.

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

Compute $$\int\frac{1}{ax+b}d{x}$$

Compute $$\int\frac{1}{x^2-a^x}d{x}$$

Compute $$\int\frac{1}{\sqrt{a^2-x^2}}d{x}$$

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

Compute $$\int\frac{\ln{x}}{x}dx$$

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

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

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

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

Evaluate $$\int\frac{5x+6}{x^2+3x+1}dx$$

Evaluate $$\int\frac{5x+6}{(x^2+x+2)^2}dx$$