Question

Integration of (x^11/2) dx​

Answer 1

$\large{❏} {\large{\boxed{\sf{∫\frac{1}{x²-6x+11}.dx}}}}$

$\large{=} {\large{\boxed{\sf{∫\frac{1}{x²-6x+9+2}.dx}}}}$

$\large{=} {\large{\boxed{\sf{∫\frac{1}{(x-3)²+(\sqrt{2})²}.dx}}}}$

❏ ${\large{\boxed{\red{\sf{∫\frac{1}{x²+a²}.dx=\frac{1}{a}Tan^{-1} (\frac{x}{a})+c}}}}}$

❏$\large{=}{\large{\boxed{\sf{\frac{1}{\sqrt{2}}Tan^{-1} (\frac{x-3}{\sqrt{2}})+c}}}}$

Answer 2

Answer:

$\int {x}^{ \frac{11}{2} }dx$

$= \frac{x {}^{\frac{11}{2} + 1} }{ \frac{11}{2} + 1}$

$= \frac{x {}^{ \frac{11 + 2}{2} } }{ \frac{11 + 2}{2} }$

$= \frac{x {}^{ \frac{13}{2} } }{ \frac{13}{2} }$

$= \frac{2}{13} (x {}^{ \frac{13}{2} }) + c$

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Note :

$\int x {}^{n}dx = \frac{x {}^{n + 1} }{n + 1} (n ≠ - 1)$

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