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.

32 questions · Easy -1.3

1.08b Integrate x^n: where n != -1 and sums
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OCR MEI AS Paper 2 Specimen Q1
3 marks Easy -1.2
1 Find \(\int \left( x ^ { 2 } + \frac { 1 } { x ^ { 2 } } \right) \mathrm { d } x\).
OCR MEI Paper 1 2023 June Q3
3 marks Easy -1.2
3 Find \(\int \left( 2 x ^ { 4 } - x \sqrt { x } \right) d x\).
OCR MEI Paper 2 2018 June Q7
4 marks Easy -1.2
7 Find \(\int \left( 4 \sqrt { x } - \frac { 6 } { x ^ { 3 } } \right) \mathrm { d } x\). Answer all the questions
Section B (79 marks)
Edexcel C1 Q2
3 marks Easy -1.2
2. Find $$\int \left( 4 x ^ { 2 } - \sqrt { x } \right) \mathrm { d } x$$
AQA C2 2007 June Q1
8 marks Easy -1.3
1
  1. Simplify:
    1. \(x ^ { \frac { 3 } { 2 } } \times x ^ { \frac { 1 } { 2 } }\);
    2. \(x ^ { \frac { 3 } { 2 } } \div x\);
    3. \(\left( x ^ { \frac { 3 } { 2 } } \right) ^ { 2 }\).
    1. Find \(\int 3 x ^ { \frac { 1 } { 2 } } \mathrm {~d} x\).
    2. Hence find the value of \(\int _ { 1 } ^ { 9 } 3 x ^ { \frac { 1 } { 2 } } \mathrm {~d} x\).
AQA AS Paper 2 2021 June Q3
3 marks Easy -1.8
3 It is given that $$\frac { \mathrm { d } y } { \mathrm {~d} x } = \sqrt { x }$$ Find an expression for \(y\).
[0pt] [3 marks]
L
AQA AS Paper 2 2022 June Q1
1 marks Easy -2.0
1 Find \(\int 12 x ^ { 3 } \mathrm {~d} x\) Circle your answer. \(36 x ^ { 2 } + c\) \(3 x ^ { 4 } + c\) \(3 x ^ { 2 } + c\) \(36 x ^ { 4 } + c\)