What is the integral of (sqrt(x)-e^x) ?

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

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integral of (sqrt(x)-e^x)

\int (x - e^{x}) d x

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

Solution steps

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

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

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

= \frac{2}{3} x^{\frac{3}{2}} - e^{x}

Add a constant to the solution

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

\int \frac{1}{x ^{2} + a ^{2}} d x

\frac{1}{s ^{2} - 2 s + 4}

x \frac{d y}{d x} - 4 y = 0

e^{4 x}

\int \frac{1}{x ( 1 + 4 ln ^{2} ( x ) )} d x

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