Section 5.7 Integration strategy (TI7)
Learning Outcomes
I can select appropriate strategies for integration.
Activity 5.7.1.
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?
The method of substitution
The method of integration by parts
Trigonometric substitution
Using a table of integrals
The method of partial fractions
Activity 5.7.2.
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?
The method of substitution
The method of integration by parts
Trigonometric substitution
Using a table of integrals
The method of partial fractions
Activity 5.7.3.
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?
The method of substitution
The method of integration by parts
Trigonometric substitution
Using a table of integrals
The method of partial fractions
Activity 5.7.4.
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?
The method of substitution
The method of integration by parts
Trigonometric substitution
Using a table of integrals
The method of partial fractions
Activity 5.7.5.
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?
The method of substitution
The method of integration by parts
Trigonometric substitution
Using a table of integrals
The method of partial fractions
Activity 5.7.6.
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?
The method of substitution
The method of integration by parts
Trigonometric substitution
Using a table of integrals
The method of partial fractions