What is the integral of 3x*e^x ?

The integral of 3x*e^x is 3(e^xx-e^x)+C

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integral of 3x*e^x

\int 3 x \cdot e^{x} d x

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

Solution steps

\int 3 x 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 e^{x} d x

Apply Integration By Parts

: e^{x} x - \int e^{x} d x

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

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

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

Add a constant to the solution

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

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

\int_{- 4}^{0} (\frac{y}{4} + y + 5) d y

\int sin^{2} (3 x) cos^{2} (3 x) d x

\frac{( 2 x ^{2} + 16 x + x ^{3^{\frac{1}{2}}} + 5 )}{x ^{3}}

\frac{d ^{2} y}{d x ^{2}} - 2 a \frac{d y}{d x} + a^{2} y = 0