Find indefinite integral of polynomial/power

4 Find \(\int \left( 20 x ^ { 4 } + 6 x ^ { - \frac { 3 } { 2 } } \right) \mathrm { d } x\).

6 Find \(\int \left( x ^ { \frac { 1 } { 2 } } + \frac { 6 } { x ^ { 3 } } \right) \mathrm { d } x\).

7 Find \(\int \left( x ^ { 3 } + \frac { 1 } { x ^ { 3 } } \right) \mathrm { d } x\).

1. Find

$$\int \left( 8 x ^ { 3 } + 4 \right) d x$$ giving each term in its simplest form.

1 Find \(\int \left( 20 x ^ { 4 } + 6 x ^ { - \frac { 3 } { 2 } } \right) \mathrm { d } x\).
[0pt] [4]

1 Find \(\int \left( x - \frac { 3 } { x ^ { 2 } } \right) \mathrm { d } x\).

2 Find \(\int \left( 3 x ^ { 5 } + 2 x ^ { - \frac { 1 } { 2 } } \right) \mathrm { d } x\).

2 Find \(\int \left( x ^ { 5 } + 10 x ^ { \frac { 3 } { 2 } } \right) \mathrm { d } x\).

1 Find \(\int 30 x ^ { \frac { 3 } { 2 } } \mathrm {~d} x\).

1. Find

$$\int \left( \frac { 2 } { 3 } x ^ { 3 } - 6 \sqrt { x } + 1 \right) \mathrm { d } x$$ giving your answer in its simplest form.

1. Find

$$\int \left( 8 x ^ { 3 } - \frac { 3 } { 2 \sqrt { x } } + 5 \right) \mathrm { d } x$$ giving your answer in simplest form.

1. Find

$$\int \left( \frac { 1 } { 2 } x ^ { 2 } - 9 \sqrt { x } + 4 \right) d x$$ giving your answer in its simplest form.

4 Find \(\int \left( 9 x ^ { 2 } + \frac { 6 } { \sqrt { x } } \right) \mathrm { d } x\).

1 Find \(\int \left( x ^ { 2 } + \frac { 1 } { x ^ { 2 } } \right) \mathrm { d } x\).

3 Find \(\int \left( 2 x ^ { 4 } - x \sqrt { x } \right) d x\).

7 Find \(\int \left( 4 \sqrt { x } - \frac { 6 } { x ^ { 3 } } \right) \mathrm { d } x\). Answer all the questions
Section B (79 marks)

2. Find $$\int \left( 4 x ^ { 2 } - \sqrt { x } \right) \mathrm { d } x$$

1. Find

$$\int \left( 3 x ^ { 2 } + \frac { 1 } { 2 x ^ { 2 } } \right) \mathrm { d } x$$

3. Find \(\int \left( 5 x ^ { \frac { 1 } { 4 } } + 3 x ^ { - 2 } - 2 \right) \mathrm { d } x\).

1

1. Simplify:
   1. \(x ^ { \frac { 3 } { 2 } } \times x ^ { \frac { 1 } { 2 } }\);
   2. \(x ^ { \frac { 3 } { 2 } } \div x\);
   3. \(\left( x ^ { \frac { 3 } { 2 } } \right) ^ { 2 }\).
2. 1. Find \(\int 3 x ^ { \frac { 1 } { 2 } } \mathrm {~d} x\).
   2. Hence find the value of \(\int _ { 1 } ^ { 9 } 3 x ^ { \frac { 1 } { 2 } } \mathrm {~d} x\).

1 Given that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 } { 6 x ^ { 2 } }\) find \(y\).
Circle your answer.
[0pt] [1 mark]
\(\frac { - 1 } { 3 x ^ { 3 } } + c\)
\(\frac { 1 } { 2 x ^ { 3 } } + c\)
\(\frac { - 1 } { 6 x } + c\)
\(\frac { - 1 } { 3 x } + c\)

3 It is given that $$\frac { \mathrm { d } y } { \mathrm {~d} x } = \sqrt { x }$$ Find an expression for \(y\).
[0pt] [3 marks]
L

1 Find \(\int 12 x ^ { 3 } \mathrm {~d} x\)
Circle your answer.
\(36 x ^ { 2 } + c\)
\(3 x ^ { 4 } + c\)
\(3 x ^ { 2 } + c\)
\(36 x ^ { 4 } + c\)

4 Find $$\int \left( x ^ { 2 } + x ^ { \frac { 1 } { 2 } } \right) \mathrm { d } x$$