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Find $$\int \left( 3x^2 - \frac{4}{x} \right) dx$$ giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 5 - 2013 - Paper 2

Question 5

$Find-$$\int-\left(-3x^2---\frac{4}{x}-\right)-dx$$-giving-each-term-in-its-simplest-form.-Edexcel-A-Level Maths Pure-Question 5-2013-Paper 2.png$

Find $$\int \left( 3x^2 - \frac{4}{x} \right) dx$$ giving each term in its simplest form.

Worked Solution & Example Answer:Find $$\int \left( 3x^2 - \frac{4}{x} \right) dx$$ giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 5 - 2013 - Paper 2

Step 1

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Answer

To integrate the term $3x^2$ , we apply the power rule of integration:

$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C,$ for $n \neq -1$ .

Thus,

$\int 3x^2 \, dx = 3 \cdot \frac{x^{3}}{3} = x^{3}.$

Step 2

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Answer

For the term $-\frac{4}{x}$ , we recognize it as $-4x^{-1}$ . The integral of this term is:

$\int -4x^{-1} \, dx = -4 \ln |x|.$

Therefore,

$\int -\frac{4}{x} \, dx = -4 \ln |x|.$

Step 3

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Answer

Combining both results, we get:

$\int \left( 3x^2 - \frac{4}{x} \right) dx = x^3 - 4 \ln |x| + C,$

where $C$ is the constant of integration.

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