What is the integral of e^{3x}(3+9x) ?

The integral of e^{3x}(3+9x) is 3e^{3x}x+C

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integral of e^{3x}(3+9x)

\int e^{3 x} (3 + 9 x) d x

3 e^{3 x} x + C

Solution steps

\int e^{3 x} (3 + 9 x) d x

Apply Integration By Parts

: e^{3 x} (3 x + 1) - \int 3 e^{3 x} d x

= e^{3 x} (3 x + 1) - \int 3 e^{3 x} d x

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

= e^{3 x} (3 x + 1) - e^{3 x}

Simplify

e^{3 x} (3 x + 1) - e^{3 x} : 3 e^{3 x} x

= 3 e^{3 x} x

Add a constant to the solution

= 3 e^{3 x} x + C

3 x + 4

n = 2 \sum \infty \frac{n}{2 ^{n}}

- u

\frac{d y}{d x} y = 3 x^{3} - 8 x^{2} + π

\int \frac{csc ^{2} ( x )}{cot ^{5} ( x )} d x

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