What is the integral of (x-3)sqrt(x+3) ?

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

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integral of (x-3)sqrt(x+3)

\int (x - 3) x + 3 d x

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

Solution steps

\int (x - 3) x + 3 d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

f (x) = 4 - x

n = 0 \sum \infty 2^{n + 1} - 2^{n}

\frac{d y}{d x} + 2 y = 1, y (0) = \frac{5}{2}

\int \frac{x - 1}{x ^{3} - 2 x ^{2}} d x

y = arcsin (3 5 x)

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