What is the integral from 0 to 1 of (x^2+x)/x ?

The integral from 0 to 1 of (x^2+x)/x is 3/2

Popular >

integral from 0 to 1 of (x^2+x)/x

\int_{0}^{1} \frac{x ^{2} + x}{x} d x

\frac{3}{2}

Solution steps

\int_{0}^{1} \frac{x ^{2} + x}{x} d x

Expand

\frac{x ^{2} + x}{x} : \frac{x ^{2}}{x} + \frac{x}{x}

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} \frac{x ^{2}}{x} d x + \int_{0}^{1} \frac{x}{x} d x

\int_{0}^{1} \frac{x ^{2}}{x} d x = \frac{1}{2}

\int_{0}^{1} \frac{x}{x} d x = 1

= \frac{1}{2} + 1

Simplify

\frac{1}{2} + 1 : \frac{3}{2}

= \frac{3}{2}

\int_{- \infty}^{0} e^{12 x} d x

\int_{0}^{\frac{π}{6}} sin^{3} (6 x) d x

\int_{0}^{2} \frac{1}{2} x^{3} d x

\int_{1}^{5} 2 π y (5 - y) d y

\int_{- 3}^{3} (2 - x)^{5} d x

What is the integral from 0 to 1 of (x^2+x)/x ?
The integral from 0 to 1 of (x^2+x)/x is 3/2