Evaluate $\int (x-6)^{\frac{5}{2}}dx$ using $u$ substitution

Question

Section 5.2. Will somebody verify this solution for me? Thanks

Evaluate $\int (x-6)^{\frac{5}{2}}dx$ using $u$ substitution

Let $u=x-6$. Then $\frac{d}{dx} u = \frac{d}{dx}(x-6)=1$.

Thus $\frac{du}{dx}=1$

"Multiplying" both sides of this equation by $dx$ we get:

$du=dx$

Thus $\int (x-6)^{\frac{5}{2}}dx=\int u^{\frac{5}{2}} du = \frac{u^{\frac{7}{2}}}{\frac{7}{2}} + C=\frac{2u^{\frac{7}{2}}}{7} + C$

Answer 1

Yes, this is correct (and revert the substitution in the end!). Please consider using an online-calculator (like WolframAlpha or SymbolLab) for verifying your solutions instead of asking multiple question of the same kind within a short preiod of time (see here and here).