What is the integral from 2 to 4 of ((6+x^2)/(x^3)) ?

The integral from 2 to 4 of ((6+x^2)/(x^3)) is 9/16+ln(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 4 of ((6+x^2)/(x^3))

\int_{2}^{4} (\frac{6 + x ^{2}}{x ^{3}}) d x

\frac{9}{16} + ln (2)

Decimal Notation

1.25564 \dots

Solution steps

\int_{2}^{4} \frac{6 + x ^{2}}{x ^{3}} d x

Expand

\frac{6 + x ^{2}}{x ^{3}} : \frac{6}{x ^{3}} + \frac{1}{x}

= \int_{2}^{4} \frac{6}{x ^{3}} + \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_{2}^{4} \frac{6}{x ^{3}} d x + \int_{2}^{4} \frac{1}{x} d x

\int_{2}^{4} \frac{6}{x ^{3}} d x = \frac{9}{16}

\int_{2}^{4} \frac{1}{x} d x = ln (2)

= \frac{9}{16} + ln (2)

x \to 0 + lim (ln (x^{2}))

\frac{d}{d x} (a x^{2} + b y (x)^{2})

\int (x^{3} + 2 x - 1) d x

a^{3} + cos^{3} (x)

y = ∣ 5 x ∣, y = x^{2} - 6

What is the integral from 2 to 4 of ((6+x^2)/(x^3)) ?
The integral from 2 to 4 of ((6+x^2)/(x^3)) is 9/16+ln(2)