What is the integral of sqrt(x+1)+2/3 x ?

The integral of sqrt(x+1)+2/3 x is 2/3 (x+1)^{3/2}+(x^2)/3+C

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integral of sqrt(x+1)+2/3 x

\int x + 1 + \frac{2}{3} x d x

\frac{2}{3} (x + 1)^{\frac{3}{2}} + \frac{x ^{2}}{3} + C

Solution steps

\int x + 1 + \frac{2}{3} 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 x + 1 d x + \int \frac{2}{3} x d x

\int x + 1 d x = \frac{2}{3} (x + 1)^{\frac{3}{2}}

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

= \frac{2}{3} (x + 1)^{\frac{3}{2}} + \frac{x ^{2}}{3}

Add a constant to the solution

= \frac{2}{3} (x + 1)^{\frac{3}{2}} + \frac{x ^{2}}{3} + C

x \to + 0 + lim (\frac{2}{1 + ln ( x )})

y = 4 x - x^{2}

\int 20 t (5 t^{2} - 3)^{3} d t

n = 5 \sum \infty \frac{1}{n ln ( n )}

\frac{d}{d x} (\frac{( 2 x ^{3} + 7 ) ( 3 x ^{2} - 5 )}{x ^{2} + 1})

What is the integral of sqrt(x+1)+2/3 x ?
The integral of sqrt(x+1)+2/3 x is 2/3 (x+1)^{3/2}+(x^2)/3+C