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

The integral of (1+e^x)x is x^2+e^xx-(x^2)/2-e^x+C

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integral of (1+e^x)x

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

x^{2} + e^{x} x - \frac{x ^{2}}{2} - e^{x} + C

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

\frac{d y}{d x} = 6 x^{7} y^{2} - \frac{y}{x}

x \to - 4 + lim (\frac{∣ x + 4 ∣}{x + 4})

y = 2 e^{k x}

\int (tan (x) - cot (x))^{2} d x

(x - 3)^{2} + (y - 1)^{2} = 0

What is the integral of (1+e^x)x ?
The integral of (1+e^x)x is x^2+e^xx-(x^2)/2-e^x+C