Find
\[
\int \left(2x^5 - \frac{1}{4}x^{-2} - 5\right) dx
\]
giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 3 - 2017 - Paper 1
Question 3
Find
\[
\int \left(2x^5 - \frac{1}{4}x^{-2} - 5\right) dx
\]
giving each term in its simplest form.
Worked Solution & Example Answer:Find
\[
\int \left(2x^5 - \frac{1}{4}x^{-2} - 5\right) dx
\]
giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 3 - 2017 - Paper 1
Step 1
Step 1: Integrate the first term
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Answer
The integral of (2x^5) is given by:
[
\int 2x^5 dx = \frac{2}{6}x^{6} = \frac{1}{3}x^{6}
]
Step 2
Step 2: Integrate the second term
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Answer
The integral of (-\frac{1}{4}x^{-2}) is:
[
\int -\frac{1}{4}x^{-2} dx = -\frac{1}{4} \cdot \left(-x^{-1}\right) = \frac{1}{4}x^{-1} = \frac{1}{4x}
]
Step 3
Step 3: Integrate the third term
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Answer
The integral of (-5) is:
[
\int -5 dx = -5x
]
Step 4
Step 4: Combine the results and add the constant of integration
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Answer
Combining all the integrated terms gives:
[
\frac{1}{3}x^{6} + \frac{1}{4x} - 5x + C
]where (C) is the constant of integration.
![Find-\[-\int-\left(2x^5---\frac{1}{4}x^{-2}---5\right)-dx-\]-giving-each-term-in-its-simplest-form.-Edexcel-A-Level Maths Pure-Question 3-2017-Paper 1.png](https://cdn.simplestudy.io/assets/backend/uploads/question/MathsPure_2017_1_1_QP_1_2017 .jpg)
