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CBSE Class 12 Math 2026 All Sets Solved Paper

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Question : 8 of 20
Marks: +1, -0
If ∫3axb2+c2x2dx=Alog⁡∣b2+c2x2∣+K\int \frac{3 a x}{b^{2} + \frac{c^{2}}{x^{2}}} dx = A \log \left| b^{2} + c^{2} x^{2} \right| + K, then the value of A is
Solution:  
∫3axb2+c2x2dx\int \frac{3 a x}{b^{2} + \frac{c^{2}}{x^{2}}} dx
u=b2+c2x2u = b^{2} + c^{2} x^{2}
du=2c2xdxd u = 2 c^{2} x dx
∫3axb2+c2x2=3a2c2∫1udu\int \frac{3 a x}{b^{2} + \frac{c^{2}}{x^{2}}} = \frac{3 a}{2 c^{2}} \int \frac{1}{u} du
=3a2c2ln⁡∣u∣+k= \frac{3 a}{2 c^{2}} \ln \left| u \right| + k
=3a2c2ln⁡∣b2+c2x2∣+k= \frac{3 a}{2 c^{2}} \ln \left| b^{2} + \frac{c^{2}}{x^{2}} \right| + k
⇒A=3a2c2.\Rightarrow A = \frac{3 a}{2 c^{2}}.
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