What is the integral of 3(x+10)e^x ?

The integral of 3(x+10)e^x is 3(e^xx+9e^x)+C

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integral of 3(x+10)e^x

\int 3 (x + 10) e^{x} d x

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

Solution steps

\int 3 (x + 10) e^{x} d x

Take the constant out:

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

= 3 \cdot \int (x + 10) e^{x} d x

Apply Integration By Parts

: e^{x} (x + 10) - \int e^{x} d x

= 3 (e^{x} (x + 10) - \int e^{x} d x)

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

= 3 (e^{x} (x + 10) - e^{x})

Expand

e^{x} (x + 10) - e^{x} : e^{x} x + 9 e^{x}

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

Add a constant to the solution

= 3 (e^{x} x + 9 e^{x}) + C

\frac{d}{d x} (e^{(\frac{x}{2})})

x \to 0 - lim (\frac{24}{tan ( x )})

x \to 1 + lim (x)

\frac{d}{d x} ((1 + x^{2}) arctan (x))

x^{3} y - y^{2}

What is the integral of 3(x+10)e^x ?
The integral of 3(x+10)e^x is 3(e^xx+9e^x)+C