Chapter 5.3, Problem 1QCE

Indicate the $u\text{-}$ substitution.

(a) ${\displaystyle \int 3x^2{\left(1+x^3\right)}^{25}x}={\displaystyle \int u^{25}du}$ if $u=\text{\_\_\_\_\_\_\_}$ and $du=\text{\_\_\_\_\_\_\_}$ .

(b) ${\displaystyle \int 2x\sin x^{2}dx}={\displaystyle \int \sin udu}$ if $u=\text{\_\_\_\_\_\_\_}$ and $du=\text{\_\_\_\_\_\_\_}$ .

(c) ${\displaystyle \int \frac{18x}{1+9x^2}dx}={\displaystyle \int \frac{1}{u}du}$ if $u=\text{\_\_\_\_\_\_\_}$ and $du=\text{\_\_\_\_\_\_\_}$ .

(d) ${\displaystyle \int \frac{3}{1+9x^2}dx}={\displaystyle \int \frac{1}{1+u^2}du}$ if $u=\text{\_\_\_\_\_\_\_}$ and $du=\text{\_\_\_\_\_\_\_}$ .