Calculus for Team-Based Inquiry Learning: PREVIEW Edition — Instructor Version

Consider the integral \(\displaystyle\int e^t \tan(e^t) \sec^2(e^t)\,dt\text{.}\) Which strategy is a reasonable first step to make progress towards evaluating this integral?

Consider the integral \(\displaystyle\int \frac{2x+3}{1+x^2}\,dx\text{.}\) Which strategy is a reasonable first step to make progress towards evaluating this integral?

Consider the integral \(\displaystyle\int \frac{x}{\sqrt[3]{1-x^2}}\,dx\text{.}\) Which strategy is a reasonable first step to make progress towards evaluating this integral?

Consider the integral \(\displaystyle\int \frac{1}{2x\sqrt{1-36x^2}}\,dx\text{.}\) Which strategy is a reasonable first step to make progress towards evaluating this integral?

Consider the integral \(\displaystyle\int t^5\cos(t^3)\,dt\text{.}\) Which strategy is a reasonable first step to make progress towards evaluating this integral?

Consider the integral \(\displaystyle\int \frac{1}{1+e^x}\,dx\text{.}\) Which strategy is a reasonable first step to make progress towards evaluating this integral?