Question

Solve the question in the above attachment .

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Answer 1

0.5 air 0.6 ka ghaunrfal kaya ha

Answer 2

Question:

integrate (5x + 2)/(3x^2 - 9x + 10) dx

Answer:

$\frac{5}{6} \sf{ln|3x {}^{2} - 9x + 10|} + \frac{19 \sqrt{39} }{39} tan {}^{ -1 } (\frac{2 \sqrt{39} x- 3 \sqrt{39} }{13} ) + C$

Step-by-step explanation:

$\int \frac{5x + 2}{3x {}^{2} - 9x + 10 }dx \\ \\ \int \frac{ 5x - \frac{15}{2} + \frac{15}{2} + 2}{3( {x} ^{2} - 3x + \frac{10}{3} ) } dx\\ \\ \frac{1}{3} \int \frac{5 x - \frac{15}{2} }{ {x}^{2} - 3x + \frac{10}{3} } dx+ \frac{1}{3} \int \frac{ \frac{15}{2} + 2}{ (x - \frac{3}{2} {)}^{2} - \frac{3 {}^{2} }{ {2}^{2} } + \frac{10}{3} } dx \\ \\ \frac{1}{3} \int \frac{ \frac{5}{2} ({2x} - 3 )}{ {x}^{2} - 3x + \frac{10}{3} } dx+ \frac{1}{3} \int \frac{\frac{19}{2}}{ (x - \frac{3}{2} {)}^{2} + \frac{13}{12} } dx \\ \\ \frac{5}{6} \int \frac{f'(x)}{f(x)}dx + \frac{19}{6} \int \frac{1}{(x - \frac{3}{2} {)}^{2} + ( \frac{ \sqrt{13} }{ \sqrt{12} } ) {}^{2} } dx \\ \\ \frac{5}{6} \sf{ln}|x{}^{2} - 3x + \frac{10}{3} | + C" + \frac{19}{6}( \frac{ \sqrt{12} }{ \sqrt{13} }) tan {}^{ - 1} \frac{x - \frac{3}{2} }{ \frac{ \sqrt{13} }{ \sqrt{12} } } + C' \\ \\ \frac{5}{6} \sf{ln|3x {}^{2} - 9x + 10| - ln|3|} + C" + \frac{19 \sqrt{39} }{39} tan {}^{ -1 } (\frac{2 \sqrt{39} x- 3 \sqrt{39} }{13} )+ C'\\\\\frac{5}{6} \sf{ln|3x {}^{2}-9x + 10|} +\frac{19 \sqrt{39} }{39} tan {}^{ -1 } (\frac{2 \sqrt{39} x-3 \sqrt{39} }{13} ) + C$