Learning Materials
Features
Discover
Chapter 11: Problem 889
\(\int[\mathrm{dx} /(1+\tan \mathrm{x})]=\underline{ }+\mathrm{c}\) (a) \(\log |\sec x+\tan x|\) (b) \(2 \sec ^{2}(\mathrm{x} / 2)\) (c) \(\log \mid \mathrm{x}+\sin \mathrm{x}\) (d) \((1 / 2)[x+\log |\sin x+\cos x|]\)
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
\(\int e^{x}\left[\left(x^{3}-x-2\right) /\left(x^{2}+1\right)^{2}\right] d x=\) (a) \(e^{x}\left[(2 x-1) /\left(x^{2}+1\right)\right]\) (b) \(e^{x}\left[(x+1) /\left(x^{2}+1\right)\right]\) (c) \(e^{x}\left[(x-1) /\left(x^{2}+1\right)\right]\) (b) \(e^{x}\left[(2 x-2) /\left(x^{2}+1\right)\right]\)
\(\int\left[\mathrm{d} \mathrm{x} /\left\\{\mathrm{x}\left(\mathrm{x}^{\mathrm{n}}+1\right)\right\\}\right]=\mathrm{c}\) (a) \((1 / n) \log \left[\left(x^{n}+1\right) / x^{n}\right] \mid\) (b) \((1 / n) \log \left|\left[x^{n} /\left(x^{n}+1\right)\right]\right|\) (c) \((1 / n) \log \left|x^{n}+1\right|\) (d) \((1 / n) \log \left|\left[\left(x^{n}-1\right) / x^{n}\right]\right|\)
\(\int\left[(\log x) / x^{2}\right] d x=\) (a) \([(-1) / x]\left(\log _{\mathrm{e}} \mathrm{x}+1\right)\) (b) \((1 / \mathrm{x})\left(\log _{\mathrm{e}} \mathrm{x}+1\right)\) (c) \(\log _{\mathrm{e}} \mathrm{x}+1\) (d) \(-\left(1+\log _{\mathrm{e}} \mathrm{x}\right)\)
\(\int\left[\mathrm{dx} /\left(\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{x}}\right)\right]=\underline{\mathrm{c}}\) (a) \(\log \left|\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{x}}\right|\) (b) \(\tan ^{-1}\left(\mathrm{e}^{\mathrm{x}}\right)\) (c) \(\log \left|\mathrm{e}^{\mathrm{x}}+1\right|\) (d) \(\tan ^{-1}\left(\mathrm{e}^{-\mathrm{x}}\right)\)
\(\int\left[\left(\mathrm{e}^{\mathrm{x}}-1\right) /\left(\mathrm{e}^{\mathrm{x}}+1\right)\right]\left[\mathrm{d} \mathrm{x} / \sqrt{ \left.\left(\mathrm{e}^{\mathrm{x}}+1+\mathrm{e}^{-\mathrm{x}}\right)\right]}=\mathrm{c}\right.\) (a) \(\tan ^{-1}\left(\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{x}}\right)\) (b) \(\sec ^{-1}\left(e^{x}+e^{-x}\right)\) (c) \(2 \tan ^{-1}\left(\mathrm{e}^{(\mathrm{x} / 2)}+\mathrm{e}^{-(\mathrm{x} / 2)}\right)\) (d) \(2 \sec ^{-1}\left(e^{(x / 2)}+e^{-(x / 2)}\right)\)
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App