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

The integral from x+2 to 2x of (y+3) is 2x^2-((x+2)^2)/2+3x-6

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integral from x+2 to 2x of (y+3)

\int_{x + 2}^{2 x} (y + 3) d y

2 x^{2} - \frac{( x + 2 ) ^{2}}{2} + 3 x - 6

Solution steps

\int_{x + 2}^{2 x} y + 3 d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{x + 2}^{2 x} y d y + \int_{x + 2}^{2 x} 3 d y

\int_{x + 2}^{2 x} y d y = 2 x^{2} - \frac{( x + 2 ) ^{2}}{2}

\int_{x + 2}^{2 x} 3 d y = 3 x - 6

= 2 x^{2} - \frac{( x + 2 ) ^{2}}{2} + 3 x - 6

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What is the integral from x+2 to 2x of (y+3) ?
The integral from x+2 to 2x of (y+3) is 2x^2-((x+2)^2)/2+3x-6