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

The integral of e^{2x}(1-3x) is -3/2 e^{2x}x+5/4 e^{2x}+C

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integral of e^{2x}(1-3x)

\int e^{2 x} (1 - 3 x) d x

- \frac{3}{2} e^{2 x} x + \frac{5}{4} e^{2 x} + C

Solution steps

\int e^{2 x} (1 - 3 x) d x

Apply Integration By Parts

: \frac{1}{2} e^{2 x} (1 - 3 x) - \int - \frac{3}{2} e^{2 x} d x

= \frac{1}{2} e^{2 x} (1 - 3 x) - \int - \frac{3}{2} e^{2 x} d x

\int - \frac{3}{2} e^{2 x} d x = - \frac{3}{4} e^{2 x}

= \frac{1}{2} e^{2 x} (1 - 3 x) - (- \frac{3}{4} e^{2 x})

Simplify

\frac{1}{2} e^{2 x} (1 - 3 x) - (- \frac{3}{4} e^{2 x}) : - \frac{3}{2} e^{2 x} x + \frac{5}{4} e^{2 x}

= - \frac{3}{2} e^{2 x} x + \frac{5}{4} e^{2 x}

Add a constant to the solution

= - \frac{3}{2} e^{2 x} x + \frac{5}{4} e^{2 x} + C

x \to 4 lim (e^{x})

\frac{d}{d a} (sin (a) - cos (a))

- \frac{sin ( x )}{cos ( x )}

x^{^{'}} - 10 x = 0

y^{^{''}} - 12 y^{^{'}} + 36 y = 30 x + 2

What is the integral of e^{2x}(1-3x) ?
The integral of e^{2x}(1-3x) is -3/2 e^{2x}x+5/4 e^{2x}+C