Integration and Accumulation of Change

The degree of the numerator is less than the degree of the denominator.

The degree of the numerator is equal to the degree of the denominator.

The denominator is a constant.

The numerator is a constant.

$x^2 + 2x + 5\ln|x - 1| + C$

$x^2 - 2x + 5\ln|x - 1| + C$

$2x^2 + 2x + 5\ln|x - 1| + C$

$x^2 + 2x - 5\ln|x - 1| + C$

$\frac{x^2}{2} - \frac{1}{2}\ln(x^2 + 1) + C$

$\frac{x^2}{2} + \frac{1}{2}\ln(x^2 + 1) + C$

$x^2 - \ln(x^2 + 1) + C$

$\frac{x^2}{2} - \ln(x^2 + 1) + C$

$x^2 + 6x + 9$

$x^2 - 4$

$x^2 + 4x + 1$

$x^2$

$\frac{1}{2}\arctan(\frac{x+1}{2}) + C$

$\arctan(\frac{x+1}{2}) + C$

$\frac{1}{2}\arcsin(\frac{x+1}{2}) + C$

$\arcsin(\frac{x+1}{2}) + C$

$\arcsin(\frac{x-1}{3}) + C$

$\frac{1}{3}\arcsin(\frac{x-1}{3}) + C$

$\arctan(\frac{x-1}{3}) + C$

$\frac{1}{3}\arctan(\frac{x-1}{3}) + C$

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

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

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

$$\int \frac{1}{x + 1} dx$$

$$\int \frac{x^3 + 1}{x^2 + 4x + 4} dx$$

$$\int \frac{x}{x^2 + 4x + 4} dx$$

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

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