What is the integral from 1 to 4 of 3xe^x ?

The integral from 1 to 4 of 3xe^x is 9e^4

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integral from 1 to 4 of 3xe^x

\int_{1}^{4} 3 x e^{x} d x

9 e^{4}

Decimal Notation

491.38335 \dots

Solution steps

\int_{1}^{4} 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_{1}^{4} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{1}^{4}

= 3 [e^{x} x - \int e^{x} d x]_{1}^{4}

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

= 3 [e^{x} x - e^{x}]_{1}^{4}

Compute the boundaries:

3 e^{4}

= 3 \cdot 3 e^{4}

Simplify

= 9 e^{4}

\int_{1}^{5} \frac{ln ( R )}{R ^{2}} d R

\frac{\partial}{\partial x} (- \frac{1}{x ^{2}})

\frac{d y}{d x} = (x + y - 5)^{2}

\int 1 + y^{2} d y

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

What is the integral from 1 to 4 of 3xe^x ?
The integral from 1 to 4 of 3xe^x is 9e^4