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

The integral of (x+x^3)/x-e^x is x+(x^3)/3-e^x+C

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

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

x + \frac{x ^{3}}{3} - e^{x} + C

Solution steps

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

\int \frac{x + x ^{3}}{x} d x = x + \frac{x ^{3}}{3}

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

= x + \frac{x ^{3}}{3} - e^{x}

Add a constant to the solution

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

What is the integral of (x+x^3)/x-e^x ?
The integral of (x+x^3)/x-e^x is x+(x^3)/3-e^x+C