What is the integral from 1 to 3 of (xy^2+x^2+y+4) ?

The integral from 1 to 3 of (xy^2+x^2+y+4) is 8+2y+26/3+y^2*4

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integral from 1 to 3 of (xy^2+x^2+y+4)

\int_{1}^{3} (x y^{2} + x^{2} + y + 4) d x

8 + 2 y + \frac{26}{3} + y^{2} \cdot 4

Solution steps

\int_{1}^{3} x y^{2} + x^{2} + y + 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

= \int_{1}^{3} 4 d x + \int_{1}^{3} y d x + \int_{1}^{3} x^{2} d x + \int_{1}^{3} y^{2} x d x

\int_{1}^{3} 4 d x = 8

\int_{1}^{3} y d x = 2 y

\int_{1}^{3} x^{2} d x = \frac{26}{3}

\int_{1}^{3} y^{2} x d x = y^{2} \cdot 4

= 8 + 2 y + \frac{26}{3} + y^{2} \cdot 4

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What is the integral from 1 to 3 of (xy^2+x^2+y+4) ?
The integral from 1 to 3 of (xy^2+x^2+y+4) is 8+2y+26/3+y^2*4