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

The integral of (x+1)^{1/2}x is 2/3 x(x+1)^{3/2}-4/15 (x+1)^{5/2}+C

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integral of (x+1)^{1/2}x

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

\frac{2}{3} x (x + 1)^{\frac{3}{2}} - \frac{4}{15} (x + 1)^{\frac{5}{2}} + C

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{2}{3} (x + 1)^{\frac{3}{2}} d x = \frac{4}{15} (x + 1)^{\frac{5}{2}}

= \frac{2}{3} x (x + 1)^{\frac{3}{2}} - \frac{4}{15} (x + 1)^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{3} x (x + 1)^{\frac{3}{2}} - \frac{4}{15} (x + 1)^{\frac{5}{2}} + C

x \to 2 lim (\frac{7}{( x - 2 ) ^{2}})

cos (x) y^{^{'}} + sin (x) y = 2 cos^{3} (x) sin (x) - 1

x \to \infty lim (3)

f (x) = tan^{2} (sin (θ))

f (x) = 2 x^{3} - 8 x, at x = 2

What is the integral of (x+1)^{1/2}x ?
The integral of (x+1)^{1/2}x is 2/3 x(x+1)^{3/2}-4/15 (x+1)^{5/2}+C