What is the integral from 0 to 1 of (1/y+sqrt(x)) ?

The integral from 0 to 1 of (1/y+sqrt(x)) is 1/y+2/3

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integral from 0 to 1 of (1/y+sqrt(x))

\int_{0}^{1} (\frac{1}{y} + x) d x

\frac{1}{y} + \frac{2}{3}

Solution steps

\int_{0}^{1} \frac{1}{y} + x 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_{0}^{1} \frac{1}{y} d x + \int_{0}^{1} x d x

\int_{0}^{1} \frac{1}{y} d x = \frac{1}{y}

\int_{0}^{1} x d x = \frac{2}{3}

= \frac{1}{y} + \frac{2}{3}

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

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\int_{0}^{5} \frac{x ^{2}}{( 5 + 2 x ) ^{2}} d x

\int_{e}^{e^{10}} \frac{1}{x ln ( x )} d x

What is the integral from 0 to 1 of (1/y+sqrt(x)) ?
The integral from 0 to 1 of (1/y+sqrt(x)) is 1/y+2/3