What is the integral of ((3x+1)^2)/(244) ?

The integral of ((3x+1)^2)/(244) is 1/244 (3x^3+3x^2+x)+C

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integral of ((3x+1)^2)/(244)

\int \frac{( 3 x + 1 ) ^{2}}{244} d x

\frac{1}{244} (3 x^{3} + 3 x^{2} + x) + C

Solution steps

\int \frac{( 3 x + 1 ) ^{2}}{244} d x

Take the constant out:

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

= \frac{1}{244} \cdot \int (3 x + 1)^{2} d x

Expand

(3 x + 1)^{2} : 9 x^{2} + 6 x + 1

= \frac{1}{244} \cdot \int 9 x^{2} + 6 x + 1 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

= \frac{1}{244} (\int 9 x^{2} d x + \int 6 x d x + \int 1 d x)

\int 9 x^{2} d x = 3 x^{3}

\int 6 x d x = 3 x^{2}

\int 1 d x = x

= \frac{1}{244} (3 x^{3} + 3 x^{2} + x)

Add a constant to the solution

= \frac{1}{244} (3 x^{3} + 3 x^{2} + x) + C

\frac{d}{d θ} (sin (θ) + θ cos (θ))

\frac{\partial}{\partial x} (2 sin (3 x + 2 y))

\int \frac{y + 1}{y} d y

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

y \to - 1 lim (- y^{5} - 3 y^{4})

What is the integral of ((3x+1)^2)/(244) ?
The integral of ((3x+1)^2)/(244) is 1/244 (3x^3+3x^2+x)+C