What is the integral of xe^{3x+1} ?

The integral of xe^{3x+1} is 1/3 e^{3x+1}x-1/9 e^{3x+1}+C

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integral of xe^{3x+1}

\int x e^{3 x + 1} d x

\frac{1}{3} e^{3 x + 1} x - \frac{1}{9} e^{3 x + 1} + C

Solution steps

\int x e^{3 x + 1} d x

Apply Integration By Parts

: \frac{1}{3} e^{3 x + 1} x - \int \frac{1}{3} e^{3 x + 1} d x

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

\int \frac{1}{3} e^{3 x + 1} d x = \frac{1}{9} e^{3 x + 1}

= \frac{1}{3} e^{3 x + 1} x - \frac{1}{9} e^{3 x + 1}

Add a constant to the solution

= \frac{1}{3} e^{3 x + 1} x - \frac{1}{9} e^{3 x + 1} + C

y = 4 x^{2}, y = 4

x \to 2 lim (- x^{2} + 4 x - 2)

\int \frac{9 x ^{3}}{x ^{2} + 1} d x

\int \frac{2 x - 3}{x ^{2} + 6 x + 4} d x

\frac{d}{d x} (13 e^{x})

What is the integral of xe^{3x+1} ?
The integral of xe^{3x+1} is 1/3 e^{3x+1}x-1/9 e^{3x+1}+C