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Find the indefinite integral.

{eq}\displaystyle \int (\frac {3}{t} - \frac {9}{t^2}) \ dt {/eq}

Question:

Find the indefinite integral.

{eq}\displaystyle \int (\frac {3}{t} - \frac {9}{t^2}) \ dt {/eq}

Evaluating indefinite integrals:

Applying sum rule we can split the given indefinite integrals into sum of smaller integrals.

Then each smaller integral is solved using integration formula for those function.

Following rules are to be used in this problem.

{eq}\begin{align} \displaystyle \text{Sum rule }&: \int (f(x)+g(x)) dx = \int f(x)dx + \int g(x)dx \\ \displaystyle \text{Inverse function integral }&: \int \frac{1}{x}dx = \ln|x|+C \\ \displaystyle \text{Inverse square function integral }&: \int \frac{1}{x^2}dx = -\frac{1}{x}+C \\ \end{align} {/eq}

Answer and Explanation: 1

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{eq}\begin{align} \text{Given integral }&=\displaystyle \int\big(\frac{3}{t}-\frac{9}{t^2}\big)dt \\ \displaystyle &=\int \frac{3}{t}dt- \int...

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Indefinite Integral: Definition, Rules & Examples

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Chapter 7 / Lesson 14
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Learn the concept and rules of indefinite and definite integrals, as well as how to find an indefinite integral through examples. View a table of integrals.


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