The document contains mathematical integrals expressed in equations. It includes: 1) An integral from 0 to infinity of (5x^2 + 9)^-1/2 dx which is evaluated to ln(u) from 14 to infinity and equals ln(infinity) - ln(14). 2) An integral from 0 to infinity of e^(x(ln(x))^2) dx which is evaluated by substituting u = ln(x) and equals -1. 3) An integral from -a to a of cos(πx) dx which equals 0.

1. Doris Perdomo
+∞ 3𝑥𝑑𝑥
10) 5 𝑥 2 +9
Sea: u= 𝑥 2 + 9 𝑑𝑢 = 2𝑥𝑑𝑢 𝑑𝑢 = 𝑥𝑑𝑥
+∞ +∞ +∞
𝑑𝑢 1 𝑑𝑢 1 1
= = ln 𝑢 = 𝑙𝑛 + ∞ − 𝑙𝑛14
14 2𝑢 2 14 𝑢 2 14 2
+∞ 𝑑𝑥 𝑑𝑥
14) 𝑒 𝑥(𝑙𝑛𝑥 )2
Sea: u= lnx du= 𝑥
∞
𝑑𝑢 1 1
= 𝑢−2 𝑑𝑢 = 𝑢−1 = − = −1
1 𝑢2 1 1 ∞ 1
+𝑎 +∞
21) −𝑎
𝑐𝑜𝑠𝜋. 𝑥𝑑𝑥 − 𝑠𝑒𝑛𝜋𝑥 −𝑎
= − 𝑠𝑒𝑛𝜋∞ − 𝑠𝑒𝑛𝜋∞ = 0
16 𝑑𝑥 16 −3 1 16
27) 0 4 𝑥3
= 0
𝑥 4 𝑑𝑥 = 4𝑥 4
0
= 4 2−0 =8
4 𝑥𝑑𝑥 𝑑𝑢
29) 0 16−𝑥 2
= 𝑆𝑒𝑎 = 𝑢 = 16𝑥 2 du=-2xdx − 2
= 𝑥𝑑𝑥
1 16
𝑑𝑢 1 0
−1 1 1 0
2 16 = − 0−4 =4
− 1 =− 𝑢 2 𝑑𝑢 = − 2𝑢
2 0 𝑢 2 2 16 2