Find the indefinite integral: {eq}\int \frac{(x^4 + x - 9)}{( x^2 + 3)} dx{/eq}

Question:

Indefinite Integrals

We split the given function into pieces in order to simplify the solution

We assume u is equal to some value and substitute in the function and integrate the function

And after integration we again replace u value

Formulas Used

{eq}\displaystyle \begin{align} \int f\left(x\right)\pm g\left(x\right)dx&=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\ \int a\cdot f\left(x\right)dx&=a\cdot \int f\left(x\right)dx\\ \int \frac{1}{u}du&=\ln \left(\left|u\right|\right)\\ \int x^adx&=\frac{x^{a+1}}{a+1}\\ \end{align} {/eq}

Answer and Explanation: 1