What is the integral of 3(3x+2) ?

The integral of 3(3x+2) is 3((3x^2)/2+2x)+C

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integral of 3(3x+2)

\int 3 (3 x + 2) d x

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

Solution steps

\int 3 (3 x + 2) d x

Take the constant out:

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

= 3 \cdot \int 3 x + 2 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

= 3 (\int 3 x d x + \int 2 d x)

\int 3 x d x = \frac{3 x ^{2}}{2}

\int 2 d x = 2 x

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

Add a constant to the solution

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

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

x \to 2 π - lim (x csc (x))

\frac{d}{d x} (5 x^{2} + 4)

x \to - 5 lim (∣ x + 5 ∣)

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