http://alnasiry.net/forums/uploaded/19175_mu3.jpg
http://alnasiry.net/forums/uploaded/19175_mu3.jpg
$\int \frac{x^{2}}{1+x^{6}}dx$
$=\frac{1}{3}\int \frac{3x^{2}}{1+(x^{3})^{2}}dx$
$=\frac{1}{3}arctan(x^{3})+c$
السلام عليكم ورحمة الله
$\LARGE {\color{DarkBlue} \int \frac{sinx}{cosx(1+cos^{2}x)}dx=\int \frac{tanx*sec^{2}x}{sec^{2}x+1}dx=\frac{1}{2}ln|sec^{2}x+1|+c}$
السلام عليكم ورحمة الله وبركاته ياموجهنا الكبير ابو احمد
نضع y=cosx ونستخدم الكسور الجزئيه
http://alnasiry.net/forums/uploaded/18045_21467056807.jpg
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https://i.imgur.com/ppdtUmy.jpg
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https://i.imgur.com/36qCISa.jpg
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$\large {\color{DarkBlue} \int \frac{1}{\sqrt{1-sin2x}}dx=\int \frac{1}{\sqrt{(sinx-cosx)^{2}}}}$
$ {\color{DarkBlue} =\int \frac{1}{\sqrt{2}}\frac{1}{sin(x-\pi/4)}dx=1/\sqrt{2}\int...
$Q41)\lim_{x\to0}\frac{e^{5x}-1}{ln(1+4x)}$
$Q42)\lim_{x\to0}\frac{\sqrt{3}sin(x+\frac{\pi }{6})-cos(x+\frac{\pi }{6})}{\sqrt{3}x(\sqrt{3}cosx-sinx)}$
$\int_{0}^{\pi}\frac{xsinx}{2-sin^{2}x}dx$
$I=\int_{0}^{\pi}\frac{xsinx}{2-sin^{2}x}dx.......(1)$
$I=\int_{0}^{\pi}\frac{(\pi -x)sin(\pi -x)}{2-sin^{2}(\pi -x)}dx\rightarrow...
https://i.imgur.com/1UUA8sO.jpg
https://i.imgur.com/eN7PhBd.jpg
السؤال التاسع
http://alnasiry.net/forums/uploaded/18045_01466108446.gif
بسم الله . بعد الحل الجميل للاستاذ مصطفى سعفان المحترم , ارفق حل س8 بطريقة ثانية .
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https://i.imgur.com/B9ehqUL.jpg
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http://im80.gulfup.com/FIykUr.png
http://im65.gulfup.com/5BMxEo.png
http://up.top4top.net/downloadf-top4top_d755191adf1-pdf.html
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