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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

3 + ln (2)

Decimal

3.69314 \dots

Solution steps

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

Expand

\frac{2 x ^{2} + 1}{x} : 2 x + \frac{1}{x}

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

\int_{1}^{2} 2 x d x = 3

\int_{1}^{2} \frac{1}{x} d x = ln (2)

= 3 + ln (2)

\int_{1}^{7} (x^{2} - 8 x + 16)^{2} d x

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

\int_{0}^{2 π} - 2 sin^{2} (t) d t

\int_{- 3}^{3} \frac{sin ( x )}{1 + x ^{2}} d x

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

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