What is the integral of (2x+3)e^{2x} ?

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

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integral of (2x+3)e^{2x}

\int (2 x + 3) e^{2 x} d x

e^{2 x} x + e^{2 x} + C

Solution steps

\int (2 x + 3) e^{2 x} d x

Apply Integration By Parts

: e^{2 x} x + \frac{3}{2} e^{2 x} - \int e^{2 x} d x

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

Add similar elements:

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

= e^{2 x} x + e^{2 x}

Add a constant to the solution

= e^{2 x} x + e^{2 x} + C

\frac{d}{d t} (e^{2 t} cos (4 t))

f (x) = (x^{4}) x^{2} + 2

\int \frac{48 x}{( x + 1 ) ^{2} ( 3 x + 1 )} d x

t^{2} y^{^{''}} - t (t + 2) y^{^{'}} + (t + 2) y = 0

y = 4 x^{2} + 3 x (- 3.27)

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