What is the integral of sqrt(x+y) ?

The integral of sqrt(x+y) is 2/3 (y+x)^{3/2}+C

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integral of sqrt(x+y)

\int x + y d x

\frac{2}{3} (y + x)^{\frac{3}{2}} + C

Solution steps

\int x + y d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = y + x

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

Add a constant to the solution

= \frac{2}{3} (y + x)^{\frac{3}{2}} + C

f (x) = sin (8 e^{x})

\int (3 x^{2} y) d x

sin^{2} (x), sin^{3} (x), [0, 2 π]

y^{^{'}} = \frac{x ^{8} - 8 y}{x}

f (x) = x + x

What is the integral of sqrt(x+y) ?
The integral of sqrt(x+y) is 2/3 (y+x)^{3/2}+C