What is the integral from a to 2a of (ax-(a^3)/x) ?

The integral from a to 2a of (ax-(a^3)/x) is a(2a^2-(a^2)/2)-ln(2)a^3

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integral from a to 2a of (ax-(a^3)/x)

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

a (2 a^{2} - \frac{a ^{2}}{2}) - ln (2) a^{3}

Solution steps

\int_{a}^{2 a} a x - \frac{a ^{3}}{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_{a}^{2 a} a x d x - \int_{a}^{2 a} \frac{a ^{3}}{x} d x

\int_{a}^{2 a} a x d x = a (2 a^{2} - \frac{a ^{2}}{2})

\int_{a}^{2 a} \frac{a ^{3}}{x} d x = ln (2) a^{3}

= a (2 a^{2} - \frac{a ^{2}}{2}) - ln (2) a^{3}

x \to \infty lim (4 e^{- 4 x})

\int x^{\frac{6}{5}} d x

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

\frac{d}{d x} (3 x^{4} - 2 x^{2} + 8)

\frac{d y}{d x} = x^{6} y^{- 3}, y (0) = 4

What is the integral from a to 2a of (ax-(a^3)/x) ?
The integral from a to 2a of (ax-(a^3)/x) is a(2a^2-(a^2)/2)-ln(2)a^3