Integrales.docx
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1) 3
𝑥
a)∫ 𝑥 − 3 𝑑𝑥 = 3 ln|𝑥| −
𝑥2 6
b)∫(4𝑥 + 2)(𝑥 − 1)𝑑𝑥 = c)∫ d)∫
(ln(𝑥))2 𝑥
+𝐶
4𝑥 3 3
− 𝑥 2 − 2𝑥 + 𝐶
1
𝑑𝑥 = 3 𝑙𝑛3 (𝑥) + 𝐶
𝑥 3 −2𝑥 3 +4𝑥 𝑑𝑥 𝑥
=
𝑥3 3
− 𝑥 2 + 4𝑥 + 𝐶
5𝑥
e)∫ 5𝑥 𝑑𝑥 = +𝐶 ln(5) 2) a)∫ 𝑥 2 (𝑥 3 − 1)10 𝑑𝑥 =
1 (𝑥 3 33
− 1)11 + 𝐶
2𝑥+1
b)∫ 𝑥 2 +𝑥+1 𝑑𝑥 = ln|𝑥 2 + 𝑥 + 1| + 𝐶 c)∫(𝑥 2 − 𝑥 − 1)(2𝑥 − 1)𝑑𝑥 =
2𝑥 4 3
−
𝑥4 6
− 𝑥3 − 𝑥2 +
𝑥2 2
+𝑥+𝐶
2
d)∫ 2𝑥𝑒 𝑥2 𝑑𝑥 = 𝑒 𝑥 + 𝐶 2
5
4
3
e)∫ 𝑥 √𝑥 + 2 𝑑𝑥 = (𝑥 + 2)2 − (𝑥 + 2)2 + 𝐶 5 3 3) 1 𝑥
a)ln 𝑥 𝑥 − ∫ 𝑥 𝑑𝑥 ln(𝑥) 𝑥 − ∫
𝑥 1 𝑑𝑥 1 𝑥 𝑥
ln(𝑥) 𝑥 − ∫ 𝑥 𝑑𝑥 ln(𝑥) 𝑥 − ∫ 1𝑑𝑥
ln(x)x−x+C 1
b)∫ 𝑥 3 𝑒 −𝑥.2 𝑑𝑥 = 16 (−8𝑒 −2𝑥 𝑥 3 − 3(4𝑒 −2𝑥 𝑥 2 − 2(−2𝑒 −2𝑥 𝑥 − 𝑒 −2𝑥 ))) + 𝑐 1
5
c)∫(𝑥 3 + 5𝑥 2 − 2)𝑒 2𝑥 𝑑𝑥 = 16 (8𝑒 2𝑥 𝑥 2 − 3(4𝑒 2𝑥 𝑥 2 − 2(2𝑒 2𝑥 𝑥 − 𝑒 2𝑥 ))) + 4 𝑒 2𝑥 (2𝑥 2 − 2𝑥 + 1) − 𝑒 2𝑥 + 𝐶
𝑥
a)∫ 𝑥 − 3 𝑑𝑥 = 3 ln|𝑥| −
𝑥2 6
b)∫(4𝑥 + 2)(𝑥 − 1)𝑑𝑥 = c)∫ d)∫
(ln(𝑥))2 𝑥
+𝐶
4𝑥 3 3
− 𝑥 2 − 2𝑥 + 𝐶
1
𝑑𝑥 = 3 𝑙𝑛3 (𝑥) + 𝐶
𝑥 3 −2𝑥 3 +4𝑥 𝑑𝑥 𝑥
=
𝑥3 3
− 𝑥 2 + 4𝑥 + 𝐶
5𝑥
e)∫ 5𝑥 𝑑𝑥 = +𝐶 ln(5) 2) a)∫ 𝑥 2 (𝑥 3 − 1)10 𝑑𝑥 =
1 (𝑥 3 33
− 1)11 + 𝐶
2𝑥+1
b)∫ 𝑥 2 +𝑥+1 𝑑𝑥 = ln|𝑥 2 + 𝑥 + 1| + 𝐶 c)∫(𝑥 2 − 𝑥 − 1)(2𝑥 − 1)𝑑𝑥 =
2𝑥 4 3
−
𝑥4 6
− 𝑥3 − 𝑥2 +
𝑥2 2
+𝑥+𝐶
2
d)∫ 2𝑥𝑒 𝑥2 𝑑𝑥 = 𝑒 𝑥 + 𝐶 2
5
4
3
e)∫ 𝑥 √𝑥 + 2 𝑑𝑥 = (𝑥 + 2)2 − (𝑥 + 2)2 + 𝐶 5 3 3) 1 𝑥
a)ln 𝑥 𝑥 − ∫ 𝑥 𝑑𝑥 ln(𝑥) 𝑥 − ∫
𝑥 1 𝑑𝑥 1 𝑥 𝑥
ln(𝑥) 𝑥 − ∫ 𝑥 𝑑𝑥 ln(𝑥) 𝑥 − ∫ 1𝑑𝑥
ln(x)x−x+C 1
b)∫ 𝑥 3 𝑒 −𝑥.2 𝑑𝑥 = 16 (−8𝑒 −2𝑥 𝑥 3 − 3(4𝑒 −2𝑥 𝑥 2 − 2(−2𝑒 −2𝑥 𝑥 − 𝑒 −2𝑥 ))) + 𝑐 1
5
c)∫(𝑥 3 + 5𝑥 2 − 2)𝑒 2𝑥 𝑑𝑥 = 16 (8𝑒 2𝑥 𝑥 2 − 3(4𝑒 2𝑥 𝑥 2 − 2(2𝑒 2𝑥 𝑥 − 𝑒 2𝑥 ))) + 4 𝑒 2𝑥 (2𝑥 2 − 2𝑥 + 1) − 𝑒 2𝑥 + 𝐶
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