What is the integral of (sqrt(x)+sqrt(a))^2 ?

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

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integral of (sqrt(x)+sqrt(a))^2

\int (x + a)^{2} d x

\frac{x ^{2}}{2} + \frac{4}{3} a x^{\frac{3}{2}} + a x + C

Solution steps

\int (x + a)^{2} d x

Expand

(x + a)^{2} : x + 2 a x + a

= \int x + 2 a x + a 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 x d x + \int 2 a x d x + \int a d x

\int x d x = \frac{x ^{2}}{2}

\int 2 a x d x = \frac{4}{3} a x^{\frac{3}{2}}

\int a d x = a x

= \frac{x ^{2}}{2} + \frac{4}{3} a x^{\frac{3}{2}} + a x

Add a constant to the solution

= \frac{x ^{2}}{2} + \frac{4}{3} a x^{\frac{3}{2}} + a x + C

7 + cot (x) - 2 csc (x)

\frac{d y}{d x} = - 3 - 2 x - y

\int \frac{1}{- x ^{2} + 8 x - 12} d x

\frac{d}{d x} (- \frac{I n ( x ^{3} )}{x})

x^{5} + x^{2} y + 9 y^{2} = 13

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