What is the integral of e^{3x+5}*(9x+5) ?

The integral of e^{3x+5}*(9x+5) is e^5(3e^{3x}x+2/3 e^{3x})+C

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integral of e^{3x+5}*(9x+5)

\int e^{3 x + 5} \cdot (9 x + 5) d x

e^{5} (3 e^{3 x} x + \frac{2}{3} e^{3 x}) + C

Solution steps

\int e^{3 x + 5} (9 x + 5) d x

e^{3 x + 5} (9 x + 5) = e^{5} e^{3 x} (9 x + 5)

= \int e^{5} e^{3 x} (9 x + 5) d x

Take the constant out:

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

= e^{5} \cdot \int e^{3 x} (9 x + 5) d x

Apply Integration By Parts

: \frac{1}{3} e^{3 x} (9 x + 5) - \int 3 e^{3 x} d x

= e^{5} (\frac{1}{3} e^{3 x} (9 x + 5) - \int 3 e^{3 x} d x)

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

= e^{5} (\frac{1}{3} e^{3 x} (9 x + 5) - e^{3 x})

Expand

\frac{1}{3} e^{3 x} (9 x + 5) - e^{3 x} : 3 e^{3 x} x + \frac{2}{3} e^{3 x}

= e^{5} (3 e^{3 x} x + \frac{2}{3} e^{3 x})

Add a constant to the solution

= e^{5} (3 e^{3 x} x + \frac{2}{3} e^{3 x}) + C

8^{^{'}}

\int \frac{8}{x ln ( 3 x )} d x

x \to - 2 lim (\frac{1}{x})

\int 8 x (4 x^{2} + 3)^{2} d x

f (x) = \frac{5}{x}, at x = 4

What is the integral of e^{3x+5}*(9x+5) ?
The integral of e^{3x+5}*(9x+5) is e^5(3e^{3x}x+2/3 e^{3x})+C