What is the integral from 1 to 2 of (6/(x^3)+2x) ?

The integral from 1 to 2 of (6/(x^3)+2x) is 21/4

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integral from 1 to 2 of (6/(x^3)+2x)

\int_{1}^{2} (\frac{6}{x ^{3}} + 2 x) d x

\frac{21}{4}

Decimal Notation

5.25

Solution steps

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

\int_{1}^{2} \frac{6}{x ^{3}} d x = \frac{9}{4}

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

= \frac{9}{4} + 3

Simplify

\frac{9}{4} + 3 : \frac{21}{4}

= \frac{21}{4}

x \to 2 lim (x^{3} - x^{2} + 2 x)

\frac{1}{2 s ^{2} + 10 s + 12}

\int x^{\frac{1}{3}} d x

\frac{d}{d x} (ln (1 + e^{- x}))

\int \frac{5 x}{1 + x ^{4}} d x

What is the integral from 1 to 2 of (6/(x^3)+2x) ?
The integral from 1 to 2 of (6/(x^3)+2x) is 21/4