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Popular >

integral of 2(3x-4)

Solution

\int 2 (3 x - 4) d x

Solution

3 x^{2} - 8 x + C

Solution steps

\int 2 (3 x - 4) d x

Take the constant out:

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

= 2 \cdot \int 3 x - 4 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

= 2 (\int 3 x d x - \int 4 d x)

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

\int 4 d x = 4 x

= 2 (\frac{3 x ^{2}}{2} - 4 x)

Simplify

2 (\frac{3 x ^{2}}{2} - 4 x) : 3 x^{2} - 8 x

= 3 x^{2} - 8 x

Add a constant to the solution

= 3 x^{2} - 8 x + C

Popular Examples

(\partial)/(\partial x)(e^{x^2y}*2yx)

\frac{\partial}{\partial x} (e^{x^{2} y} \cdot 2 y x)

derivative of x^{sqrt(x)}+2^xln(x)

\frac{d}{d x} (x^{x} + 2^{x} ln (x))

integral of (x-4)/x

\int \frac{x - 4}{x} d x

area x,x^2-2,-1,4 area

x, x^{2} - 2, - 1, 4

limit as x approaches 4 of sqrt(x)+2

x \to 4 lim (x + 2)

Frequently Asked Questions (FAQ)

What is the integral of 2(3x-4) ?
The integral of 2(3x-4) is 3x^2-8x+C