What is the integral of ((sqrt(x)-x^3e^x+x^2)/(x^3)) ?

The integral of ((sqrt(x)-x^3e^x+x^2)/(x^3)) is -2/(3x^{3/2)}-e^x+ln|x|+C

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integral of ((sqrt(x)-x^3e^x+x^2)/(x^3))

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

- \frac{2}{3 x ^{\frac{3}{2}}} - e^{x} + ln ∣ x ∣ + C

Solution steps

\int \frac{x - x ^{3} e ^{x} + x ^{2}}{x ^{3}} d x

Expand

\frac{x - x ^{3} e ^{x} + x ^{2}}{x ^{3}} : \frac{1}{x ^{\frac{5}{2}}} - e^{x} + \frac{1}{x}

= \int \frac{1}{x ^{\frac{5}{2}}} - e^{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 \frac{1}{x ^{\frac{5}{2}}} d x - \int e^{x} d x + \int \frac{1}{x} d x

\int \frac{1}{x ^{\frac{5}{2}}} d x = - \frac{2}{3 x ^{\frac{3}{2}}}

\int e^{x} d x = e^{x}

\int \frac{1}{x} d x = ln ∣ x ∣

= - \frac{2}{3 x ^{\frac{3}{2}}} - e^{x} + ln ∣ x ∣

Add a constant to the solution

= - \frac{2}{3 x ^{\frac{3}{2}}} - e^{x} + ln ∣ x ∣ + C

y^{^{'}} = \frac{1 - y ^{2}}{e ^{x}}

n = 0 \sum \infty p^{n}

x \to 3 lim (6 x)

\int \frac{q}{π ( - 0.125 x + 0.03125 ) ^{2}} d x

\int \frac{1}{2 - 2 x} d x

What is the integral of ((sqrt(x)-x^3e^x+x^2)/(x^3)) ?
The integral of ((sqrt(x)-x^3e^x+x^2)/(x^3)) is -2/(3x^{3/2)}-e^x+ln|x|+C