## What is the integration of $\int {\sqrt {5 – 2x + {x^2}} } dx$ ~~~~~[NCERT Exemp. Q. 17,Page 164 ]

Let $I = \int {\sqrt {5 - 2x + {x^2}} } dx = \int {\sqrt {{x^2} - 2x + 1 + 4} } dx$$= \int {\sqrt {{{(x -… Continue Reading What is the integration of \[ \int {\sqrt {5 – 2x + {x^2}} } dx$ ~~~~~[NCERT Exemp. Q. 17,Page 164 ]

What is the integration of $\int {\frac{{(1 + \cos x)}}{{x + \sin x}}} dx$ ~~~~~[NCERT Exemp. Q. 5,Page 164 ] Consider that, $I = \int {\frac{{(1 + \cos x)}}{{(x +… Continue Reading What is the integration of$\int {\frac{{(1 + \cos x)}}{{x + \sin x}}} dx$~~~~~[NCERT Exemp. Q. 5,Page 164 ] ## Show that $\int {\frac{{2x – 1}}{{2x + 3}}} dx = x – \log \left| {{{(2x + 3)}^2}} \right| + C$ ~~~~~[NCERT Exemp. Q. 1,Page 163 ] Let$I = \int {\frac{{2x - 1}}{{2x + 3}}} dx = \int {\frac{{2x + 3 - 3 - 1}}{{2x + 3}}} dx = \int 1 dx - 4\int {\frac{1}{{2x…

Continue Reading Show that $\int {\frac{{2x – 1}}{{2x + 3}}} dx = x – \log \left| {{{(2x + 3)}^2}} \right| + C$ ~~~~~[NCERT Exemp. Q. 1,Page 163 ]