What is the integral of e^{2x}-x^2-1 ?

The integral of e^{2x}-x^2-1 is 1/2 e^{2x}-(x^3)/3-x+C

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integral of e^{2x}-x^2-1

\int e^{2 x} - x^{2} - 1 d x

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

Solution steps

\int e^{2 x} - x^{2} - 1 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^{2 x} d x - \int x^{2} d x - \int 1 d x

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

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

\int 1 d x = x

= \frac{1}{2} e^{2 x} - \frac{x ^{3}}{3} - x

Add a constant to the solution

= \frac{1}{2} e^{2 x} - \frac{x ^{3}}{3} - x + C

\frac{d}{d x} (cos (2 x))

y^{^{'}} = y (x y^{2} + 1)

\int 4 sin^{6} (x) cos^{3} (x) d x

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

\int 4 x^{2} e^{x} d x

What is the integral of e^{2x}-x^2-1 ?
The integral of e^{2x}-x^2-1 is 1/2 e^{2x}-(x^3)/3-x+C