What is the integral of (0.1x+1)e^{0.03x} ?

The integral of (0.1x+1)e^{0.03x} is 3.33333…e^{0.03x}x-77.77777…e^{0.03x}+C

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integral of (0.1x+1)e^{0.03x}

\int (0.1 x + 1) e^{0.03 x} d x

3.33333 \dots e^{0.03 x} x - 77.77777 \dots e^{0.03 x} + C

Solution steps

\int (0.1 x + 1) e^{0.03 x} d x

Expand

(0.1 x + 1) e^{0.03 x} : 0.1 e^{0.03 x} x + e^{0.03 x}

= \int 0.1 e^{0.03 x} x + e^{0.03 x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 0.1 e^{0.03 x} x d x + \int e^{0.03 x} d x

\int 0.1 e^{0.03 x} x d x = 0.1 (33.33333 \dots e^{0.03 x} x - 1111.11111 \dots e^{0.03 x})

\int e^{0.03 x} d x = 33.33333 \dots e^{0.03 x}

= 0.1 (33.33333 \dots e^{0.03 x} x - 1111.11111 \dots e^{0.03 x}) + 33.33333 \dots e^{0.03 x}

Simplify

0.1 (33.33333 \dots e^{0.03 x} x - 1111.11111 \dots e^{0.03 x}) + 33.33333 \dots e^{0.03 x} : 3.33333 \dots e^{0.03 x} x - 77.77777 \dots e^{0.03 x}

= 3.33333 \dots e^{0.03 x} x - 77.77777 \dots e^{0.03 x}

Add a constant to the solution

= 3.33333 \dots e^{0.03 x} x - 77.77777 \dots e^{0.03 x} + C

f (x) = (x - 6) (3 x + 5)

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

\frac{d}{d x} ((x^{3} - 3 x^{2} + 1)^{- 3})

x^{3} - 9 x^{2} + 10 x, at = - 2

n = 0 \sum \infty \frac{x ^{n}}{n 3 ^{n}}

What is the integral of (0.1x+1)e^{0.03x} ?
The integral of (0.1x+1)e^{0.03x} is 3.33333…e^{0.03x}x-77.77777…e^{0.03x}+C