{"@context":"https://schema.org/","@type":"Quiz","dateCreated":"2026-05-07T11:28:57.051Z","dateModified":"2026-05-07T11:28:57.051Z","typicalAgeRange":"11-18","educationalLevel":"AP ECET Ceramic Tech","assesses":"Mathematics - integral","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalTopic","targetName":"integral"},{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"Mathematics"},{"@type":"AlignmentObject","alignmentType":"educationalExam","targetName":"AP ECET Ceramic Tech"}],"name":"Quiz about integral","about":{"@type":"Thing","name":"Mathematics - integral"},"hasPart":[{"@type":"Question","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","educationalLevel":"intermediate","name":"Question About integral","text":"$$\\displaystyle \\int \\frac{dx}{25-x^2}=$$}","encodingFormat":"text/markdown","comment":{"@type":"Comment","text":"Remember the standard formula \$\\int\\frac{dx}{a^2-x^2}=\\frac{1}{2a}\\log\\left|\\frac{a+x}{a-x}\\right|+c\$."},"suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/markdown","text":"

\$\\frac{1}{5}\\log\\left|\\frac{x-5}{x+5}\\right|+c\$

","comment":{"@type":"Comment","text":"\"\""}},{"@type":"Answer","position":1,"encodingFormat":"text/markdown","text":"

\$\\frac{1}{5}\\log\\left|\\frac{x+5}{x-5}\\right|+c\$

","comment":{"@type":"Comment","text":"\"\""}},{"@type":"Answer","position":2,"encodingFormat":"text/markdown","text":"

\$\\frac{1}{10}\\log\\left|\\frac{5+x}{5-x}\\right|+c\$

","comment":{"@type":"Comment","text":"\"\""}},{"@type":"Answer","position":3,"encodingFormat":"text/markdown","text":"

\$\\frac{1}{10}\\log\\left|\\frac{5-x}{5+x}\\right|+c\$\n\n

","comment":{"@type":"Comment","text":"\"\""}}],"acceptedAnswer":{"@type":"Answer","position":2,"encodingFormat":"text/markdown","text":"

\$\\frac{1}{10}\\log\\left|\\frac{5+x}{5-x}\\right|+c\$

","comment":{"@type":"Comment","text":"Remember the standard formula \$\\int\\frac{dx}{a^2-x^2}=\\frac{1}{2a}\\log\\left|\\frac{a+x}{a-x}\\right|+c\$."},"answerExplanation":{"@type":"comment","text":""}}}]}

\(\displaystyle \int \frac{dx}{25-x^2}=\)

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The Correct Option is C

Solution and Explanation

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