Question

Find the integral ( from 0 to 2): qdq / (8q +5) im trying to use u substitution.

Answer 1

\[\int_0^2\frac{q}{8q+5}~dq\]
Let \(u=8q+5\), so that \(\dfrac{1}{8}du=dq\). Note that \(u=8q+5~\iff~q=\dfrac{u-5}{8}\).

Now substitute into the integral, keeping in mind the change in limits:
\[\frac{1}{8}\int_5^{21}\frac{\frac{u-5}{8}}{u}~du\\
\frac{1}{64}\int_5^{21}\frac{u-5}{u}~du\\
\frac{1}{64}\int_5^{21}\left(1-\frac{5}{u}\right)~du\\
\]

Answer 2

Thank you.

Answer 3

You're welcome