What is the integral from x+1 to 2x of x ?

The integral from x+1 to 2x of x is (3x^2-2x-1)/2

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integral from x+1 to 2x of x

\int_{x + 1}^{2 x} x d x

\frac{3 x ^{2} - 2 x - 1}{2}

Solution steps

\int_{x + 1}^{2 x} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{x + 1}^{2 x}

= [\frac{x ^{2}}{2}]_{x + 1}^{2 x}

Compute the boundaries:

2 x^{2} - \frac{( x + 1 ) ^{2}}{2}

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

Simplify

= \frac{3 x ^{2} - 2 x - 1}{2}

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What is the integral from x+1 to 2x of x ?
The integral from x+1 to 2x of x is (3x^2-2x-1)/2