Noon Academy
contexto.140
3 years ago
Now putting,
Equating coefficients
….(i)
….. (ii)
![\[\left( 1-2C \right)+\frac{1-C}{2}=1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8cf86a67570e049d79db8d43da91ce6d_l3.png "Rendered by QuickLaTeX.com")
![\[2-4C+1-C=2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-77bc03f6c0c90d3870bd5ecf6f28b31d_l3.png "Rendered by QuickLaTeX.com")
![\[3-5C=2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0bc019d3bbe20dfe129dc51edb92f100_l3.png "Rendered by QuickLaTeX.com")
![\[-5C=-1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-682d5a5f443bde0bee570e8bc52e1785_l3.png "Rendered by QuickLaTeX.com")
![\[C=\frac{1}{5}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7ffabcd586c3798846e908c483ea8f21_l3.png "Rendered by QuickLaTeX.com")
![\[2B=1-\frac{1}{5}=\frac{4}{5}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1c3ab7af8b576879fac3c1ff24b99138_l3.png "Rendered by QuickLaTeX.com")
![\[B=\frac{2}{5}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-54d8b9952ba729fba550c52765106edc_l3.png "Rendered by QuickLaTeX.com")
![\[A=1-2\times \frac{1}{5}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a660a798c7cd84a9f5b86a1f37b6339a_l3.png "Rendered by QuickLaTeX.com")
![\[=1-\frac{2}{5}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f0cea9c1071ab94b694a1d9b1d366a2d_l3.png "Rendered by QuickLaTeX.com")
![\[=\frac{3}{5}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5789325960761c22147a7519b5c066ba_l3.png "Rendered by QuickLaTeX.com")
![\[I=\frac{{{x}^{2}}+x+1}{(x+2)({{x}^{2}}+1)}dx=\int \frac{A}{\left( x+2 \right)}dx+\int \frac{Bx+C}{\left( {{x}^{2}}+1 \right)}dx\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2687743e1aa0e7d771afc7b7a3f15852_l3.png "Rendered by QuickLaTeX.com")
![\[\frac{3}{5}\times \int \frac{1}{(x+2)}dx+\frac{1}{5}\times \int \frac{2x+1}{\left( {{x}^{2}}+1 \right)}dx\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-907df522002d1e93ca85ca0a2349587f_l3.png "Rendered by QuickLaTeX.com")
![\[\frac{3}{5}\log \left| x+2 \right|+\frac{1}{5}{{I}_{1}}+{{C}_{1}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3356d1c55493f89a9bd26f1495a75a55_l3.png "Rendered by QuickLaTeX.com")
![\[{{I}_{1}}=\int \frac{2x+1}{({{x}^{2}}+1)}dx=\int \frac{2x}{({{x}^{2}}+1)}dx+\int \frac{1}{({{x}^{2}}+1)}dx\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-cf0ee167e7bc53772f9560e616d3f2b3_l3.png "Rendered by QuickLaTeX.com")
![\[=\log \left| {{x}^{2}}+1 \right|+{{\tan }^{-1}}x+{{C}_{2}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-72bf8d6d3d26d6566dc97456e8d4db4d_l3.png "Rendered by QuickLaTeX.com")
![\[I=\int \frac{{{x}^{2}}+x+1}{\left( x+2 \right)\left( {{x}^{2}}+1 \right)}dx\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-eb16710175d7eea09c962fbc1aaf4921_l3.png "Rendered by QuickLaTeX.com")
![\[=\frac{3}{5}\log \left| x+2 \right|+\frac{1}{5}\log \left| {{x}^{2}}+1 \right|+\frac{1}{5}{{\tan }^{-1}}x+c\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-69a7ceb86fb526a831677e0b1d5c5c71_l3.png "Rendered by QuickLaTeX.com")
