CBSE Class 12 Mathematics 2026 Main Paper 65/3/1 · Q101 Markssubstitution
CBSE Class 12 Mathematics 2026 Main Paper 65/3/1 · Question 10 (Integrals)
Evaluate \(\int\frac{dx}{2^x+2^{-x}}\).
✅ Step-by-Step Solution
Final Answer: arctan(2ˣ)/ln 2+C
- Set u=2ˣ, so du=u ln 2 dx. The integral is (1/ln 2)∫du/(1+u²), which gives arctan(u)/ln 2+C.
Master Chapter 7: Integrals
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Integrals.
← Previous Question
Find the rate of change of a sphere’s volume with respect to…
Next Question →Which expression equals \(\int_{-1}^{1}(1-|x|)\,dx\)?
All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/3/1
Related Questions in Integrals
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int x^2e^{x^3}\,dx\).
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int e^x(1+x)\sec^2(xe^x)\,dx\) on an interval where defined.
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int e^x(\cos x-\sin x)\,dx\).
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int dx/(\sin^2x\cos^2x)\) on an interval avoiding its poles.
Class 12 Integrals · Mcq Single Correct
If \(\int\frac{3e^x-5e^{-x}}{4e^x+5e^{-x}}dx=ax+b\ln|4e^x+5e^{-x}|+C\), find a,b.
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int_{-1}^{1}|x-2|/(x-2)\,dx\).