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Questions › CUET-PG › CUET-PG 2023 Shift 1 › Q92
4 marks, −1Mathematics › Integration and its applications › Indefinite and definite integralsModerateabout 2 min

CUET-PG 2023 Shift 1 Question 92: Integration and its applications

∫(e8ln⁡x−e4ln⁡xe4ln⁡x−e2ln⁡x)dx\int \left(\frac{e^{8\ln x} - e^{4\ln x}}{e^{4\ln x} - e^{2\ln x}}\right) dx∫(e4lnx−e2lnxe8lnx−e4lnx​)dx

  1. e8x−e4xe4x−e2x+C\frac{e^{8x} - e^{4x}}{e^{4x} - e^{2x}} + Ce4x−e2xe8x−e4x​+C
  2. x55+x33+C\frac{x^5}{5} + \frac{x^3}{3} + C5x5​+3x3​+C
  3. x55−x33+C\frac{x^5}{5} - \frac{x^3}{3} + C5x5​−3x3​+C
  4. e4x−e2xe2x−ex+C\frac{e^{4x} - e^{2x}}{e^{2x} - e^{x}} + Ce2x−exe4x−e2x​+C

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Answer and worked solution

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Plain-text version

∫ ((e^(8ln x) - e^(4ln x))/(e^(4ln x) - e^(2ln x))) dx 1. (e^(8x) - e^(4x))/(e^(4x) - e^(2x)) + C 2. x⁵/5 + x³/3 + C 3. x⁵/5 - x³/3 + C 4. (e^(4x) - e^(2x))/(e^(2x) - e^x) + C (A) (e^(8x) - e^(4x))/(e^(4x) - e^(2x)) + C (B) x⁵/5 + x³/3 + C (C) x⁵/5 - x³/3 + C (D) (e^(4x) - e^(2x))/(e^(2x) - e^x) + C

Also written as: integral ((e^(8ln x) - e^(4ln x))/(e^(4ln x) - e^(2ln x))) dx 1. (e^(8x) - e^(4x))/(e^(4x) - e^(2x)) + C 2. x^5/5 + x^3/3 + C 3. x^5/5 - x^3/3 + C 4. (e^(4x) - e^(2x))/(e^(2x) - e^x) + C

Integration and its applications has come up 43 times in 6 exams since 2007.

What this question tests

This question is on Indefinite and definite integrals, part of Integration and its applications in Mathematics.

Antiderivatives and areas under curves for standard functions.

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Question from the CUET-PG 2023 Shift 1 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.