What is the integral of e^{2x}(2x+1) ?

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

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integral of e^{2x}(2x+1)

\int e^{2 x} (2 x + 1) d x

e^{2 x} x + C

Solution steps

\int e^{2 x} (2 x + 1) d x

Apply Integration By Parts

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

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

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

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

Add similar elements:

\frac{1}{2} e^{2 x} - \frac{1}{2} e^{2 x} = 0

= e^{2 x} x

Add a constant to the solution

= e^{2 x} x + C

y = \frac{- 2 x}{x ^{2} + 1}

\frac{d y}{d x} + 6 x^{5} y = x^{5}

\frac{\partial}{\partial z} (10 e^{x} sin (y) z^{3})

\frac{d}{d x} ((A x^{2} + B x + C) (e^{4 x}))

y^{^{'}} = \frac{2 y ^{4} - 2}{4 x y ^{3}}

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