What is the integral of (t-6)sqrt(t-3) ?

The integral of (t-6)sqrt(t-3) is 2/3 (t-6)(t-3)^{3/2}-4/15 (t-3)^{5/2}+C

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integral of (t-6)sqrt(t-3)

\int (t - 6) t - 3 d t

\frac{2}{3} (t - 6) (t - 3)^{\frac{3}{2}} - \frac{4}{15} (t - 3)^{\frac{5}{2}} + C

Solution steps

\int (t - 6) t - 3 d t

Apply Integration By Parts

: \frac{2}{3} (t - 6) (t - 3)^{\frac{3}{2}} - \int \frac{2}{3} (t - 3)^{\frac{3}{2}} d t

= \frac{2}{3} (t - 6) (t - 3)^{\frac{3}{2}} - \int \frac{2}{3} (t - 3)^{\frac{3}{2}} d t

\int \frac{2}{3} (t - 3)^{\frac{3}{2}} d t = \frac{4}{15} (t - 3)^{\frac{5}{2}}

= \frac{2}{3} (t - 6) (t - 3)^{\frac{3}{2}} - \frac{4}{15} (t - 3)^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{3} (t - 6) (t - 3)^{\frac{3}{2}} - \frac{4}{15} (t - 3)^{\frac{5}{2}} + C

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What is the integral of (t-6)sqrt(t-3) ?
The integral of (t-6)sqrt(t-3) is 2/3 (t-6)(t-3)^{3/2}-4/15 (t-3)^{5/2}+C