1.8.8 Integration by substitution (A-level only)

i.

Find

\int x^2e^{2x} \, dx

[4]

ii.

Use the substitution $\sqrt{2x + 1}$ to show that

\int \frac{12x}{\sqrt{2x + 1}} \, dx = 2(2x + 1)^{\frac{1}{2}}(Ax + B) + k

where $A$ and $B$ are integers to be found and $k$ is an arbitrary constant.

[6]

i.

Find

\int x^2e^{2x} \, dx

[4]

ii.

Use the substitution $\sqrt{2x + 1}$ to show that

\int \frac{12x}{\sqrt{2x + 1}} \, dx = 2(2x + 1)^{\frac{1}{2}}(Ax + B) + k

where $A$ and $B$ are integers to be found and $k$ is an arbitrary constant.

[6]

1.8.8 Integration by substitution (A-level only) Questions