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Popular >

integral of 2(2x+1)6

Solution

\int 2 (2 x + 1) 6 d x

Solution

12 (x^{2} + x) + C

Solution steps

\int 2 (2 x + 1) \cdot 6 d x

Take the constant out:

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

= 2 \cdot 6 \cdot \int 2 x + 1 d x

Simplify

= 12 \cdot \int 2 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

= 12 (\int 2 x d x + \int 1 d x)

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

\int 1 d x = x

= 12 (x^{2} + x)

Add a constant to the solution

= 12 (x^{2} + x) + C

Popular Examples

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(dy)/(dx)=-2y+x,y(0)=0

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derivative of sqrt(x)+x^2

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

integral of t^5

\int t^{5} d t

Frequently Asked Questions (FAQ)

What is the integral of 2(2x+1)6 ?
The integral of 2(2x+1)6 is 12(x^2+x)+C