I'm trying to solve the integral below:
$\int_2^8 \frac{dt}{4t+14}$
The issue for me is not calculating the integral, but the antiderivative. My steps for calculating it looked something like this:
- $\displaystyle\int_2^8 \frac{1}{2} \frac{dt}{2t+7}$
- $\displaystyle\frac{1}{2}\int_2^8 \frac{dt}{2t+7}$
- $\displaystyle\frac{1}{2}\ln(2t + 7)$
I double checked my answer with Wolfram|Alpha, but it (correctly) calculated it as:
$\frac{1}{4}\ln(2t + 7)$
I looked at the steps it took, but they don't make much sense for me. Hopefully someone can help me out with this.