Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How can I resolve this indefinite integral?

$$ \int \left({8,387x+1 \over 9,41x+1} + \sin(9,326x + 1)\right) dx $$

I'm blocked here

$$ \int\left({{8387 \over 1000}x+1}\over{{941\over100}x+1} \right)dx + \int\left(\sin\left({9326\over1000}x+1\right) \right)dx $$

please anyone can help me? thanks

share|cite|improve this question
Replace those strange numbers with some friendly ones so you do not get distracted while doing and learning the substitution method. Then apply what you learned to the general case. – Maesumi Jan 17 '13 at 13:47
up vote 4 down vote accepted

As said above, I also think you are getting distracted by the "strange" numbers.

Assume you have


where $a,b,c$ are some constants, then you can write


now just proceed by rewriting the first term as $\dfrac{a}{b}-\dfrac{a/b}{bx+1}$, this is, now you have

$\displaystyle\int\left( \dfrac{a}{b}-\dfrac{a/b}{bx+1} \right)dx+\displaystyle\int\dfrac{1}{bx+1}dx+\displaystyle\int\sin(cx+1)dx$,

and now you are able to integrate everything by declaring new variables as already suggested: $u=bx+1$ and $v=cx+1$.

share|cite|improve this answer

Do a substitution $w = 9.41 \, x + 1$ for the first and $y = 9.236 \, x + 1$ for the second integral.

share|cite|improve this answer
but how can i resolve the 8,387x+1? – Sam Jan 17 '13 at 12:39

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.