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What is the integration of $\int {\frac{{\sin x + \cos x}}{{\sqrt {1 + \sin 2x} }}} dx$ ~~~~~[NCERT Exemp. Q. 8,Page 164 ]
What is the integration of $\int {{{\tan }^2}} x{\sec ^4}xdx$ ~~~~~[NCERT Exemp. Q. 7,Page 164 ]
What is the integration of $\int {\frac{{dx}}{{1 + \cos x}}} $ ~~~~~[NCERT Exemp. Q. 6,Page 164 ]
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What is the integration of $\int {\frac{{(1 + \cos x)}}{{x + \sin x}}} dx$ ~~~~~[NCERT Exemp. Q. 5,Page 164 ]
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What is the integration of $\int {\frac{{{e^{6\log x}} – {e^{5\log x}}}}{{{e^{4\log x}} – {e^{3\log x}}}}} dx$~~~~~[NCERT Exemp. Q. 4,Page 163 ]
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What is the integration of $\int {\frac{{\left( {{x^2} + 2} \right)d}}{{x + 1}}} x$ ~~~~~[NCERT Exemp. Q. 3,Page 163 ]
Show that integration of $\int {\frac{{2x + 3}}{{{x^2} + 3x}}} dx = \log \left| {{x^2} + 3x} \right| + C$ ~~~~~[NCERT Exemp. Q. 2,Page 163 ]
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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 + 3}}} dx = x – \int {\frac{4}{{2\left( {x + \frac{3}{2}} \right)}}} dx$ $ = x – 2\log + \left| {\left( {x + \frac{3}{2}} \right)} \right|{C^\prime } = x – 2\log \left| {\left( {\frac{{2x + 3}}{2}} \right)} \right| + {C^\prime }$ $ = x – 2\log |(2x + 3)| + 2\log 2 + {C^\prime }$ $ = x – \log \left| {{{(2x + 3)}^2}} \right| + C$ Buy Best Mathematics E-Books Visit : https://mathstudy.in/ Buy Mathematics Formula Book for Class XI,XII,JEE and other Engineering Competition Exam https://mathstudy.in/product/mathematics-formula-book/ Buy Mathematics Workbook for Class XII ( Fully Solved ) : https://mathstudy.in/product/work-book-class-xii-c-b-s-e-fully-solved/ Buy Mathematics Chapter Tests for Class XII ( Fully Solved) : https://mathstudy.in/product/mathematics-chapter-tests-class-xii-c-b-s-e/ Buy Objective Type Question Bank Class XII (Fully Solved ) : https://mathstudy.in/product/objective-type-question-bank-for-mathematics-class-xii-c-b-s-e/
Find the area of the region in the first quadrant enclosed by x-axis, line x = \sqrt 3 y and the circle x^2 + y^2 = 4[ NCERT Ex. 8.1, Q.6,Page 366]
Find the area of the region in the first quadrant enclosed by x-axis, line x = \sqrt 3 y and the circle x^2 + y^2 = 4[ NCERT Ex. 8.1, Q.6,Page 366]