Calculus for Team-Based Inquiry Learning: 2023 Early Edition

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?