Solve 1/x(x+1)(x+2)dx

$$\frac { 1 } { x ( x + 1 ) ( x + 2 ) } d x$$

Evaluate

$$\frac{d}{\left(x+1\right)\left(x+2\right)}$$

Short Solution Steps

Use the distributive property to multiply x by x+1.

$$\frac{1}{\left(x^{2}+x\right)\left(x+2\right)}dx$$

Apply the distributive property by multiplying each term of x^{2}+x by each term of x+2.

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

Combine 2x^{2} and x^{2} to get 3x^{2}.

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

Express \frac{1}{x^{3}+3x^{2}+2x}d as a single fraction.

$$\frac{d}{x^{3}+3x^{2}+2x}x$$

Express \frac{d}{x^{3}+3x^{2}+2x}x as a single fraction.

$$\frac{dx}{x^{3}+3x^{2}+2x}$$

Factor the expressions that are not already factored.

$$\frac{dx}{x\left(x+1\right)\left(x+2\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{d}{\left(x+1\right)\left(x+2\right)}$$

Expand the expression.

$$\frac{d}{x^{2}+3x+2}$$

Expand

$$\frac{d}{\left(x+1\right)\left(x+2\right)}$$

Short Solution Steps

Use the distributive property to multiply x by x+1.

$$\frac{1}{\left(x^{2}+x\right)\left(x+2\right)}dx$$

Apply the distributive property by multiplying each term of x^{2}+x by each term of x+2.

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

Combine 2x^{2} and x^{2} to get 3x^{2}.

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

Express \frac{1}{x^{3}+3x^{2}+2x}d as a single fraction.

$$\frac{d}{x^{3}+3x^{2}+2x}x$$

Express \frac{d}{x^{3}+3x^{2}+2x}x as a single fraction.

$$\frac{dx}{x^{3}+3x^{2}+2x}$$

Factor the expressions that are not already factored.

$$\frac{dx}{x\left(x+1\right)\left(x+2\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{d}{\left(x+1\right)\left(x+2\right)}$$

Expand the expression.

$$\frac{d}{x^{2}+3x+2}$$