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

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

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

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

\frac{1}{2} e^{2 x} x + \frac{1}{4} e^{2 x} + C

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{1}{2} e^{2 x} d x = \frac{1}{4} e^{2 x}

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

Simplify

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

= \frac{1}{2} e^{2 x} x + \frac{1}{4} e^{2 x}

Add a constant to the solution

= \frac{1}{2} e^{2 x} x + \frac{1}{4} e^{2 x} + C

3 x^{\frac{1}{2}}

f (x) = 3 x cos (x), at x = π

\frac{\partial}{\partial x} (x^{2} + 3)

9 y^{^{''}} + 9 y = 0

3 x^{2} e^{x} + e^{x} (x^{3} + 9)

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