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

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

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

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

a^{2} - \frac{a ^{2}}{2}

Solution steps

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

\int_{a}^{2 a} a d x = a^{2}

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

= a^{2} - \frac{a ^{2}}{2}

7 ln (sec (x) + tan (x))

x \to 7 lim (c x + 8)

θ \to 0 lim (cot (θ))

\frac{\partial}{\partial y} (x^{3} y^{5} + 2 x^{4} y)

\frac{\partial}{\partial x} (- 2 cos (x))

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