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

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

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integral of (e^x+x^2-2^x)

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

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

Solution steps

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

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

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

\int 2^{x} d x = \frac{2 ^{x}}{ln ( 2 )}

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

Add a constant to the solution

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

\frac{1}{8} \frac{d ^{2} x}{d t ^{2}} = - 2 x - 1 \frac{d x}{d t}

\int (2 x - 4) (x + 2) d x

x - 4, x = 8

\frac{\partial}{\partial x} (e^{x} + z^{2})

2 (y - 4 x^{2}) d x + x d y = 0

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