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Find $$\int (8x^3 + 4) \, dx$$ giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 3 - 2014 - Paper 1

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$Find-$$\int-(8x^3-+-4)-\,-dx$$-giving-each-term-in-its-simplest-form.-Edexcel-A-Level Maths Pure-Question 3-2014-Paper 1.png$

Find $$\int (8x^3 + 4) \, dx$$ giving each term in its simplest form.

Worked Solution & Example Answer:Find $$\int (8x^3 + 4) \, dx$$ giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 3 - 2014 - Paper 1

Step 1

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Answer

To find the integral of the first term, we apply the power rule for integration:

$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$

For the term $8x^3$ , we have:

$\int (8x^3) \, dx = 8 \cdot \frac{x^{3+1}}{3+1} + C = 8 \cdot \frac{x^4}{4} + C = 2x^4 + C$

Step 2

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Answer

The integral of a constant is simply the constant multiplied by the variable of integration:

$\int 4 \, dx = 4x + C$

Step 3

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Answer

Now, we can sum the integrals of both terms:

$\int (8x^3 + 4) \, dx = 2x^4 + 4x + C$

Thus, the final answer is:

$2x^4 + 4x + C$

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