Module 8 Quiz

For $\int 2x \cos(x^2)\, dx$, the most natural substitution is:

If $u = 3x - 1$, then $dx$ equals:

Before integrating $(x + 1)/(x^2 - 1)$, a useful first step is to:

A common identity for integrating $\sin^2 x$ is:

A common identity for integrating $\cos^2 x$ is:

To integrate $\tan^2 x$, rewrite it as:

The derivative of $\sin^{-1} x$ is:

The derivative of $\cos^{-1} x$ is:

The derivative of $\tan^{-1} x$ is:

$\int dx/\sqrt{a^2 - x^2}$ equals:

$\int a/(a^2 + x^2)\, dx$ equals:

Completing the square is especially useful before integrating expressions involving:

A trigonometric substitution for $\sqrt{a^2 - x^2}$ commonly uses:

In an odd power integral such as $\int \sin^5 x \cos^2 x\, dx$, a useful strategy is to:

A reduction formula is mainly used to: