What is the integral of (2x-5)e^x ?

The integral of (2x-5)e^x is 2e^xx-7e^x+C

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integral of (2x-5)e^x

\int (2 x - 5) e^{x} d x

2 e^{x} x - 7 e^{x} + C

Solution steps

\int (2 x - 5) e^{x} d x

Apply Integration By Parts

: (2 x - 5) e^{x} - \int 2 e^{x} d x

= (2 x - 5) e^{x} - \int 2 e^{x} d x

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

= (2 x - 5) e^{x} - 2 e^{x}

Simplify

(2 x - 5) e^{x} - 2 e^{x} : 2 e^{x} x - 7 e^{x}

= 2 e^{x} x - 7 e^{x}

Add a constant to the solution

= 2 e^{x} x - 7 e^{x} + C

x \to 0 + lim (2 x^{x})

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

\frac{\partial}{\partial x} (x \cdot e^{y})

x \to \infty lim (9 x^{2} - 1)

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