What is the integral of 2x*e^{4x+2} ?

The integral of 2x*e^{4x+2} is 2(1/4 e^{4x+2}x-1/16 e^{4x+2})+C

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integral of 2x*e^{4x+2}

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

2 (\frac{1}{4} e^{4 x + 2} x - \frac{1}{16} e^{4 x + 2}) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int x e^{4 x + 2} d x

Apply Integration By Parts

: \frac{1}{4} e^{4 x + 2} x - \int \frac{1}{4} e^{4 x + 2} d x

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

\int \frac{1}{4} e^{4 x + 2} d x = \frac{1}{16} e^{4 x + 2}

= 2 (\frac{1}{4} e^{4 x + 2} x - \frac{1}{16} e^{4 x + 2})

Add a constant to the solution

= 2 (\frac{1}{4} e^{4 x + 2} x - \frac{1}{16} e^{4 x + 2}) + C

(t^{2} + t) cos (5 t)

y^{^{''}} + 4 y^{^{'}} + 4 y = - 3 e^{2 t}

n = 1 \sum \infty \frac{1}{2 ^{n + 2}}

f (x) = 18 e^{x} + 10 x, at x = 0

\int \frac{6 x}{x ^{3} - 8} d x

What is the integral of 2x*e^{4x+2} ?
The integral of 2x*e^{4x+2} is 2(1/4 e^{4x+2}x-1/16 e^{4x+2})+C