Integrals — Class 12 Maths Solution

ncert exercise SA NCERT,ex.7.2,Q.38,Page 305
Question

$\int {\left( {\cfrac{{10{x^9} + {{10}^x}{{\log }_e}10}}{{{x^{10}} + {{10}^x}}}} \right)} dx$equals

  • (a) ${10^x} - {x^{10}} + C$
  • (b) ${10^x} + {x^{10}} + C$
  • (c) ${\left( {{{10}^x} - {x^{10}}} \right)^{ - 1}} + C$
  • (d) $\log \left( {{{10}^x} + {x^{10}}} \right) + C$
Step-by-step Solution

Option d is correct

Let $I = \int {\left( {\cfrac{{10{x^9} + {{10}^x}{{\log }_e}10}}{{{x^{10}} + {{10}^x}}}} \right)} dx$

Put ${x^{10}} + {10^x} = t$ $\Rightarrow$ $\left( {10{x^9} + {{\log }_e}10 \cdot {{10}^x}} \right)dx = dt$

$\Rightarrow$ $I = \int {\cfrac{{dt}}{t} = \log \left| t \right|} + C = \log \left( {{x^{10}} + {{10}^x}} \right) + C$

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Integrals. Curated by Sachin Sharma. Free for all students.