Chapter 5.9, Problem 1ES

Express the integral in terms of the variable $u$ , but do not evaluate it.

(a) ${\displaystyle {\int }_1^3{\left(2x-1\right)}^{3}dx};u=2x-1$

(b) ${\displaystyle {\int }_0^{4}3x\sqrt{25-x^2}dx};u=25-x^2$

(c) ${\displaystyle {\int }_{-1/2}^{1/2}\cos \left(\pi \theta \right)d\theta };u=\pi \theta$

(d) ${\displaystyle {\int }_0^1\left(x+2\right){\left(x+1\right)}^{5}dx};u=x+1$