Find
\[ \int \left( 6x^{2} + \frac{2}{x} + 5 \right) dx \]
giving each term in its simplest form.
- Edexcel - A-Level Maths Pure - Question 3 - 2012 - Paper 2
Question 3
Find
\[ \int \left( 6x^{2} + \frac{2}{x} + 5 \right) dx \]
giving each term in its simplest form.
Worked Solution & Example Answer:Find
\[ \int \left( 6x^{2} + \frac{2}{x} + 5 \right) dx \]
giving each term in its simplest form.
- Edexcel - A-Level Maths Pure - Question 3 - 2012 - Paper 2
Step 1
Integrate the term $6x^{2}$
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Answer
The integral of 6x2 is [ 2x^{3} ].
Step 2
Integrate the term $\frac{2}{x}$
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Answer
The integral of x2 is [ 2\ln|x| ].
Step 3
Integrate the term $5$
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Answer
The integral of 5 is [ 5x ].
Step 4
Combine the results
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Answer
Putting it all together, we have:
[ \int \left( 6x^{2} + \frac{2}{x} + 5 \right) dx = 2x^{3} + 2\ln|x| + 5x + c ]
![Find-\[-\int-\left(-6x^{2}-+-\frac{2}{x}-+-5-\right)-dx-\]-giving-each-term-in-its-simplest-form.--Edexcel-A-Level Maths Pure-Question 3-2012-Paper 2.png](https://cdn.simplestudy.io/assets/backend/uploads/question/MathsPure_2012_2_1_QP_1_2012.jpg)
