What is the integral of sqrt(x+4y) ?

The integral of sqrt(x+4y) is 2/3 (x+4y)^{3/2}+C

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integral of sqrt(x+4y)

\int x + 4 y d x

\frac{2}{3} (x + 4 y)^{\frac{3}{2}} + C

Solution steps

\int x + 4 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 = x + 4 y

= \frac{2}{3} (x + 4 y)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (x + 4 y)^{\frac{3}{2}} + C

n = 1 \sum \infty \frac{n ^{n}}{n !}

4 \frac{d y}{d x} + 28 y = 7

\int 4 cos^{3} (2 x) d x

(x^{l n (x)})^{^{'}}

\frac{( s + 3 )}{( s ^{2} )}

What is the integral of sqrt(x+4y) ?
The integral of sqrt(x+4y) is 2/3 (x+4y)^{3/2}+C