6.9 Integrating Using Substitution

3 practice questions

Notes

Use $u$-substitution when you see a function and its derivative (up to a constant):

Let $u$ be the inside function; find $du$.
For definite integrals, change the limits to $u$-values (or switch back to $x$).

$\displaystyle \int 2x(x^2+1)^5\,dx=$

$\displaystyle \int\cos(3x)\,dx=$

With $u=x^2$, the integral $\displaystyle \int_0^2 x e^{x^2}dx$ has new limits: