Find the indefinite integral: {eq}\int \frac{(x^4 + x - 9)}{( x^2 + 3)} dx{/eq}
Question:
Find the indefinite integral: {eq}\int \frac{(x^4 + x - 9)}{( x^2 + 3)} dx{/eq}
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
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View this answer{eq}\displaystyle \int \frac{(x^4 + x - 9)}{( x^2 + 3)} dx {/eq}
{eq}\displaystyle \begin{align} \int \frac{(x^4 + x - 9)}{( x^2 + 3)} dx&=\int...
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Chapter 13 / Lesson 7Learn how to use and define integration by parts. Discover the integration by parts rule and formula. Learn when and how to use integration by parts with examples.