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
As said above, I also think you are getting distracted by the "strange" numbers.
Assume you have
$\displaystyle\int\dfrac{ax+1}{bx+1}dx+\displaystyle\int\sin(cx+1)dx$,
where $a,b,c$ are some constants, then you can write
$\displaystyle\int\dfrac{ax}{bx+1}dx+\displaystyle\int\dfrac{1}{bx+1}dx+\displaystyle\int\sin(cx+1)dx$,
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 $v=cx+1$.