Find indefinite integral of polynomial/power

A question is this type if and only if it asks to find ∫f(x)dx where f(x) contains only powers of x (including negative and fractional powers) and constants, with no other functions.

49 questions · Easy -1.4

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CAIE P1 2011 June Q1
3 marks Easy -1.2
1 Find \(\int \left( x ^ { 3 } + \frac { 1 } { x ^ { 3 } } \right) \mathrm { d } x\).
CAIE P1 2018 November Q2
4 marks Easy -1.2
2 Showing all necessary working, find \(\int _ { 1 } ^ { 4 } \left( \sqrt { } x + \frac { 2 } { \sqrt { } x } \right) \mathrm { d } x\).
Edexcel P1 2019 January Q1
4 marks Easy -1.2
  1. Find
$$\int \left( \frac { 2 } { 3 } x ^ { 3 } - \frac { 1 } { 2 x ^ { 3 } } + 5 \right) d x$$ simplifying your answer.
Edexcel P1 2020 January Q1
4 marks Easy -1.2
  1. Find, in simplest form,
$$\int \left( \frac { 8 x ^ { 3 } } { 3 } - \frac { 1 } { 2 \sqrt { x } } - 5 \right) \mathrm { d } x$$
Edexcel P1 2022 January Q1
4 marks Easy -1.2
  1. Find
$$\int \left( \frac { 8 x ^ { 3 } } { 5 } - \frac { 2 } { 3 x ^ { 4 } } - 1 \right) d x$$ giving each term in simplest form.
Edexcel P1 2022 June Q1
4 marks Easy -1.3
  1. Find
$$\int \left( 10 x ^ { 5 } + 6 x ^ { 3 } - \frac { 3 } { x ^ { 2 } } \right) \mathrm { d } x$$ giving your answer in simplest form.
Edexcel P1 2024 June Q1
3 marks Easy -1.2
  1. Find
$$\int \left( 10 x ^ { 4 } - \frac { 3 } { 2 x ^ { 3 } } - 7 \right) \mathrm { d } x$$ giving each term in simplest form.
Edexcel P1 2021 October Q1
5 marks Easy -1.2
  1. Find
$$\int 12 x ^ { 3 } + \frac { 1 } { 6 \sqrt { x } } - \frac { 3 } { 2 x ^ { 4 } } \mathrm {~d} x$$ giving each term in simplest form.
Edexcel C12 2014 January Q2
7 marks Easy -1.2
2. $$\mathrm { f } ( x ) = \frac { 8 } { x ^ { 2 } } - 4 \sqrt { x } + 3 x - 1 , \quad x > 0$$ Giving your answers in their simplest form, find
  1. \(\mathrm { f } ^ { \prime } ( x )\)
  2. \(\int \mathrm { f } ( x ) \mathrm { d } x\)
Edexcel C12 2018 January Q1
5 marks Easy -1.2
  1. Given that
$$y = \frac { 2 x ^ { \frac { 2 } { 3 } } + 3 } { 6 } , \quad x > 0$$ find, in the simplest form,
  1. \(\frac { \mathrm { d } y } { \mathrm {~d} x }\)
  2. \(\int y \mathrm {~d} x\)
Edexcel C12 2016 October Q1
5 marks Easy -1.3
1. $$f ( x ) = 3 x ^ { 2 } + x - \frac { 4 } { \sqrt { x } } + 6 x ^ { - 3 } , \quad x > 0$$ Find \(\int \mathrm { f } ( x ) \mathrm { d } x\), simplifying each term.
Edexcel C1 2008 June Q1
3 marks Easy -1.8
Find \(\int \left( 2 + 5 x ^ { 2 } \right) d x\).
Edexcel C1 Q2
4 marks Easy -1.2
2. Find \(\int \left( x ^ { 2 } - \frac { 1 } { x ^ { 2 } } + \sqrt [ 3 ] { x } \right) \mathrm { d } x\) & Leave blank
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Edexcel C1 2009 January Q2
4 marks Easy -1.8
Find \(\int \left( 12 x ^ { 5 } - 8 x ^ { 3 } + 3 \right) \mathrm { d } x\), giving each term in its simplest form.
Edexcel C1 2013 June Q3
4 marks Easy -1.3
Find $$\int \left( 3 x ^ { 2 } - \frac { 4 } { x ^ { 2 } } \right) \mathrm { d } x$$ giving each term in its simplest form.
Edexcel C2 2006 June Q2
5 marks Easy -1.2
Use calculus to find the exact value of \(\int _ { 1 } ^ { 2 } \left( 3 x ^ { 2 } + 5 + \frac { 4 } { x ^ { 2 } } \right) \mathrm { d } x\).
OCR MEI C2 2005 January Q2
4 marks Easy -1.2
2 Find \(\int \left( x ^ { 3 } + \frac { 1 } { x ^ { 3 } } \right) \mathrm { d } x\).
OCR MEI C2 2006 January Q8
5 marks Easy -1.2
8 Find \(\int \left( x ^ { \frac { 1 } { 2 } } + \frac { 6 } { x ^ { 3 } } \right) \mathrm { d } x\).
OCR MEI C2 2008 January Q5
5 marks Easy -1.3
5 Find \(\int \left( 12 x ^ { 5 } + \sqrt [ 3 ] { x } + 7 \right) \mathrm { d } x\).
OCR C2 Q1
4 marks Easy -1.2
  1. Find
$$\int \left( 3 x ^ { 2 } + \frac { 1 } { 2 x ^ { 2 } } \right) \mathrm { d } x$$
OCR MEI C2 Q1
3 marks Easy -1.8
1 Find \(\int 7 x ^ { \frac { 5 } { 2 } } \mathrm {~d} x\).
OCR MEI C2 Q11
3 marks Easy -1.8
11 Find \(\int 30 x ^ { \frac { 3 } { 2 } } \mathrm {~d} x\).
OCR MEI C2 Q12
4 marks Easy -1.3
12 Find \(\int \left( x ^ { 5 } + 10 x ^ { \frac { 3 } { 2 } } \right) \mathrm { d } x\).
OCR MEI C2 Q1
4 marks Easy -1.2
1 Find \(\int \left( 3 x ^ { 5 } + 2 x ^ { - \frac { 1 } { 2 } } \right) \mathrm { d } x\).
OCR MEI C2 Q3
3 marks Easy -1.2
3 Find \(\int \left( x - \frac { 3 } { x ^ { 2 } } \right) \mathrm { d } x\).