NCERT Class 12 · Ch 7 Exercise 7.5 · Q21
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.5 Question 21
Evaluate \(\int \frac{1}{e^{x} - 1}\, dx\).
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: \(- x + \log{\left(\left|{e^{x} - 1}\right| \right)}\) + C.
- Work on each open interval where the original integrand is real and defined.
- Let u=eˣ>0, dx=du/u; split 1/[u(u−1)]=1/(u−1)−1/u.
- An antiderivative is F(x)=\(- x + \log{\left(\left|{e^{x} - 1}\right| \right)}\).
- Differentiate this expression to check that F′(x)=\(\frac{1}{e^{x} - 1}\). Add an arbitrary constant C on each domain component.
Master Chapter 7: Integrals
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Integrals.
← Previous Question
Evaluate \(\int \frac{1}{x \left(x^{4} - 1\right)}\, dx\).
Next Question →Evaluate \(\int \frac{x}{\left(x - 2\right) \left(x - 1\right)}\…
All Questions in Integrals — Exercise 7.5
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 \(\int_{-1}^{1}|x-2|/(x-2)\,dx\).