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

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

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integral from 1 to x of (x^2y-y+2)

\int_{1}^{x} (x^{2} y - y + 2) d y

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

Solution steps

\int_{1}^{x} x^{2} y - y + 2 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_{1}^{x} 2 d y - \int_{1}^{x} y d y + \int_{1}^{x} x^{2} y d y

\int_{1}^{x} 2 d y = 2 x - 2

\int_{1}^{x} y d y = \frac{x ^{2} - 1}{2}

\int_{1}^{x} x^{2} y d y = \frac{x ^{2} ( x ^{2} - 1 )}{2}

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

\int_{0}^{4} 3 x^{3} - 3 x + 1 d x

\int_{1}^{5} \frac{7}{x} d x

\int_{2}^{x} \frac{1}{2} (x - 2) d x

\int_{0}^{3} \frac{1}{1 + x ^{3}} d x

\int_{4}^{7} \frac{1}{ln ( x )} d x

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