What is the integration of \[ \int {\sqrt {5 – 2x + {x^2}} } dx\] ~~~~~[NCERT Exemp. Q. 17,Page 164 ]
What is the integration of \[\int {\frac{{(\cos 5x + \cos 4x)}}{{1 – 2\cos 3x}}} dx\] ~~~~~[NCERT Exemp. Q. 22,Page 164 ]
What is the integration of \[\int {\frac{{{{\sin }^{ – 1}}x}}{{{{\left( {1 – {x^2}} \right)}^{3/4}}}}} dx\] ~~~~~[NCERT Exemp. Q. 21,Page 164 ]
What is the integration of \[ \int {\sqrt {2ax – {x^2}} } dx\] ~~~~~[NCERT Exemp. Q. 20,Page 164 ]
What is the integration of \[ \int {\frac{{{x^2}}}{{1 – {x^4}}}} dx\] ~~~~~[NCERT Exemp. Q. 19,Page 164 ]
What is the integration of \[ \int {\sqrt {5 – 2x + {x^2}} } dx\] ~~~~~[NCERT Exemp. Q. 17,Page 164 ]
What is the integration of \[ \int {\frac{{3x – 1}}{{\sqrt {{x^2} + 9} }}} dx\] ~~~~~[NCERT Exemp. Q. 16,Page 164 ]
Let \[ I = \int {\frac{{3x – 1}}{{\sqrt {{x^2} + 9} }}} dx\] \[I = \int {\frac{{3x}}{{\sqrt {{x^2} + 9} }}} dx – \int {\frac{1}{{\sqrt {{x^2} + 9} }}} dx\] \[ I = {I_1} – {I_2}\] Now, \[ {I_1} = \int {\frac{{3x}}{{\sqrt {{x^2} + 9} }}} \] Let’s put \[ {x^2} + 9 = {t^2} \Rightarrow 2xdx = 2tdt \Rightarrow xdx = tdt\] therefore,\[{I_1} = 3\int_t^t d t\] \[ = 3\int d t = 3t + {C_1} = 3\sqrt {{x^2} + 9} + {C_1}\] and \[ {I_2} = \int {\frac{1}{{\sqrt {{x^2} + 9} }}} dx = \int {\frac{1}{{\sqrt {{x^2} + {{(3)}^2}} }}} dx\] \[ = \log \left| {x + \sqrt {{x^2} + 9} } \right| + {C_2}\] therefore,\[ I = 3\sqrt {{x^2} + 9} + {C_1} – \log \left| {x + \sqrt {{x^2} + 9} } \right| – {C_2}\] 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/
What is the integration of \[ \int {\frac{{dt}}{{\sqrt {3t – 2{t^2}} }}} \] ~~~~~[NCERT Exemp. Q. 15,Page 164 ]
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