Indefinite Integral

Find the following integral:

    \[\int \frac{18x}{9x^{2} + 6x + 4 } \, \mathrm{d}x\]

Answer:

    \[\ln{\left(9x^{2}+6x+4\right)}-\frac{2}{3}\sqrt{3}\tan^{-1}{\left(\frac{1}{\sqrt{3}}\left(3x+1\right)\right)}+C\]

where C is an arbitrary constant.

Source: R.L. Rosenberg. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Additional Exercises in Integration: Question (xxxviii))

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

Leave a Reply