Atividade: Integrais Indefinidas de Funções

Nesta atividade, nós vamos praticar a encontrar as integrais indefinidas de funções.

Q1:

Determine ๏„ธ๏€น10๐‘ฅ+21๐‘ฅโˆ’49๏…๐‘ฅ๏Šจd.

  • A30๐‘ฅ+42๐‘ฅโˆ’49๐‘ฅ+๏Šฉ๏ŠจC
  • B10๐‘ฅ+C
  • C103๐‘ฅ+212๐‘ฅโˆ’49๐‘ฅ+๏Šฉ๏ŠจC
  • D10๐‘ฅ+21๐‘ฅโˆ’49๐‘ฅ+๏Šฉ๏ŠจC
  • E5๐‘ฅ+21๐‘ฅโˆ’49๐‘ฅ+๏Šฉ๏ŠจC

Q2:

Determine ๏„ธ๏€ผโˆ’4โˆš๐‘ฅโˆ’5+7๐‘ฅ๏ˆ๐‘ฅ๏Šจd.

  • Aโˆ’5๐‘ฅโˆ’8โˆš๐‘ฅ+7๐‘ฅ+๏ŠฉC
  • Bโˆ’4๐‘ฅ+7๐‘ฅ+๏ŠจC
  • Cโˆ’5๐‘ฅโˆ’8โˆš๐‘ฅ3โˆ’7๐‘ฅ+๏ŠฉC
  • Dโˆ’8โˆš๐‘ฅโˆ’7๐‘ฅ+C

Q3:

Determine ๏„ธ๐‘ฅโˆ’14๐‘ฅ๐‘ฅโˆ’14๐‘ฅ๏Šช๏Šฉd.

  • A3๐‘ฅ+๏ŠชC
  • B13๐‘ฅ+๏ŠชC
  • C14๐‘ฅ+๏ŠชC
  • D๐‘ฅ+๏ŠชC
  • E4๐‘ฅ+๏ŠชC

Q4:

Determine ๏„ธ๏€ผ๐‘ฅโˆ’5๐‘ฅ๏ˆ๏€ผ๐‘ฅ+5๐‘ฅ๏ˆ๏€ผ๐‘ฅ+25๐‘ฅ๏ˆ๐‘ฅ๏Šจ๏Šจd.

  • A๐‘ฅ4+6254๐‘ฅ+๏Šซ๏ŠฉC
  • B๐‘ฅ5โˆ’6253๐‘ฅ+๏Šซ๏ŠฉC
  • C๐‘ฅ5+6253๐‘ฅ+๏Šซ๏ŠฉC
  • D๐‘ฅ3+125๐‘ฅ+๏Šฉ๏ŠซC

Q5:

Determine ๏„ธ๏€ผ3๐‘ฅโˆ’7๐‘ฅ๏ˆ๐‘ฅ๏Šจd.

  • A13๏€ผ3๐‘ฅโˆ’7๐‘ฅ๏ˆ+๏ŠฉC
  • B9๐‘ฅโˆ’42๐‘ฅ+49๐‘ฅ+๏ŠฉC
  • C๏€ผ3๐‘ฅโˆ’7๐‘ฅ๏ˆ+๏ŠฉC
  • D3๐‘ฅโˆ’42๐‘ฅโˆ’49๐‘ฅ+๏ŠฉC

Q6:

Determine ๏„ธ4๐‘ฅ+๐‘ฅ+12๐‘ฅ+1๐‘ฅ๏Šฉd.

  • A6๐‘ฅโˆ’2๐‘ฅ+๐‘ฅ+๏Šฉ๏ŠจC
  • B2๐‘ฅโˆ’๐‘ฅ+๐‘ฅ+๏Šฉ๏ŠจC
  • C2๐‘ฅ3โˆ’๐‘ฅ2+๐‘ฅ+๏Šฉ๏ŠจC
  • D๐‘ฅโˆ’๐‘ฅ+๐‘ฅ+๏Šฉ๏ŠจC

Q7:

Determine ๏„ธ๏„Ÿ๏€ผ8๐‘ฅโˆ’18๐‘ฅ๏ˆ+4๐‘ฅ๏Šจ๏Šจ๏Šจd.

  • A24๐‘ฅโˆ’18๐‘ฅ+๏Šฉ๏Šฑ๏ŠงC
  • B8๐‘ฅโˆ’124๐‘ฅ+๏Šฑ๏ŠฉC
  • C8๐‘ฅ+18๐‘ฅ+๏Šฉ๏Šฑ๏ŠงC
  • D4๐‘ฅโˆ’116๐‘ฅ+๏Šฉ๏Šฑ๏ŠงC
  • E83๐‘ฅโˆ’18๐‘ฅ+๏Šฉ๏Šฑ๏ŠงC

Q8:

Determine ๏„ธ36๐‘ฅโˆ’49โˆš๐‘ฅ(6๐‘ฅ+7)๐‘ฅ๏Šจ๏Žงd.

  • A45๐‘ฅ4โˆ’49๐‘ฅ8+๏Ž ๏Žค๏Žง๏Žฆ๏ŽงC
  • B6๐‘ฅโˆ’7๐‘ฅ+๏Ž ๏Žค๏Žง๏Žฆ๏ŽงC
  • C16๐‘ฅ5โˆ’8๐‘ฅ+๏Ž ๏Žค๏Žง๏Žฆ๏ŽงC
  • D48๐‘ฅ7+56๐‘ฅ+๏Ž ๏Žค๏Žง๏Žฆ๏ŽงC

Q9:

Determine ๏„ธ(4๐‘ฅ+1)(2๐‘ฅโˆ’6)๐‘ฅd.

  • A8๐‘ฅ+C
  • B4๐‘ฅโˆ’22๐‘ฅโˆ’6๐‘ฅ+๏Šฉ๏ŠจC
  • C83๐‘ฅโˆ’11๐‘ฅโˆ’6๐‘ฅ+๏Šฉ๏ŠจC
  • D24๐‘ฅโˆ’44๐‘ฅโˆ’6๐‘ฅ+๏Šฉ๏ŠจC
  • E8๐‘ฅโˆ’22๐‘ฅโˆ’6๐‘ฅ+๏Šฉ๏ŠจC

Q10:

Determine ๏„ธ๐‘ฅโˆ’19๐‘ฅ+70๐‘ฅโˆ’14๐‘ฅ๏Šจd.

  • A12๏€น๐‘ฅโˆ’19๐‘ฅ+70๏…+๏Šจ๏ŠจC
  • B๐‘ฅ2โˆ’5๐‘ฅ+๏ŠจC
  • C๐‘ฅ3โˆ’19๐‘ฅ2+70๐‘ฅ+๏Šฉ๏ŠจC
  • D๐‘ฅ2โˆ’14๐‘ฅ+๏ŠจC

Q11:

Determine ๏„ธ(๐‘ฅ+4)๏€น๐‘ฅโˆ’4๐‘ฅ+16๏…๐‘ฅ๏Šจd.

  • A4๐‘ฅ+64๐‘ฅ+๏ŠชC
  • B๐‘ฅ4+64๐‘ฅ+๏ŠชC
  • C๐‘ฅ3+64๐‘ฅ+๏ŠชC
  • D๐‘ฅ2+64๐‘ฅ+๏ŠจC

Q12:

Determine ๏„ธ(๐‘ฅโˆ’6)(๐‘ฅโˆ’5)(๐‘ฅโˆ’3)๐‘ฅd.

  • A๐‘ฅโˆ’14๐‘ฅ+63๐‘ฅโˆ’90+๏Šฉ๏ŠจC
  • B18(๐‘ฅโˆ’6)(๐‘ฅโˆ’5)(๐‘ฅโˆ’3)+๏Šจ๏Šจ๏ŠจC
  • C๐‘ฅโˆ’14๐‘ฅ+63๐‘ฅโˆ’90๐‘ฅ+๏Šช๏Šฉ๏ŠจC
  • D๐‘ฅ4โˆ’14๐‘ฅ3+63๐‘ฅ2โˆ’90๐‘ฅ+๏Šช๏Šฉ๏ŠจC

Q13:

Determine ๏„ธโˆ’27๐‘ฅ๐‘ฅ๏Šฑ๏Šฏd.

  • A128๐‘ฅ+๏Šฑ๏ŠฎC
  • B135๐‘ฅ+๏Šฑ๏Šง๏ŠฆC
  • C167๐‘ฅ+๏Šฑ๏ŠฎC
  • Dโˆ’27๐‘ฅ+๏Šฑ๏ŠฎC
  • E263๐‘ฅ+๏Šฑ๏ŠฎC

Q14:

Determine ๏„ธโˆ’9๐‘ฅ+79๐‘ฅ๐‘ฅ๏Šจ๏Šจd.

  • A79๐‘ฅ+C
  • Bโˆ’๐‘ฅโˆ’79๐‘ฅ+๏ŠจC
  • Cโˆ’๐‘ฅ+79๐‘ฅ+C
  • Dโˆ’79๐‘ฅ+C

Q15:

Determine ๏„ธ๏’(โˆ’9๐‘ฅ+10)โˆ’8๏ž๐‘ฅ๏Šจd.

  • Aโˆ’8๐‘ฅ+13(โˆ’9๐‘ฅ+10)+๏ŠฉC.
  • Bโˆ’8๐‘ฅโˆ’127(โˆ’9๐‘ฅ+10)+๏ŠฉC.
  • Cโˆ’8๐‘ฅโˆ’18(โˆ’9๐‘ฅ+10)+๏ŠจC.
  • Dโˆ’24๐‘ฅโˆ’27(โˆ’9๐‘ฅ+10)+๏ŠฉC.

Q16:

Determine ๏„ธ๏€ผ8โˆš๐‘ฅโˆ’1๐‘ฅ๏ˆ๐‘ฅ๏Šชd.

  • A8โˆš๐‘ฅโˆ’1๐‘ฅ+๏Šฉ๏ŠฉC
  • B12โˆš๐‘ฅ+3๐‘ฅ+๏Šฉ๏ŠฉC
  • C163โˆš๐‘ฅ+13๐‘ฅ+๏Šฉ๏ŠฉC
  • D16โˆš๐‘ฅ+14๐‘ฅ+๏Šฉ๏ŠฉC
  • Eโˆ’16โˆš๐‘ฅ+15๐‘ฅ+๏ŠซC

Q17:

Determine ๏„ธ7โˆš๐‘ฅ๐‘ฅ๏Šฉd.

  • A7โˆš๐‘ฅ+๏ŠซC
  • B70โˆš๐‘ฅ+๏ŠซC
  • C14โˆš๐‘ฅ+C
  • D145โˆš๐‘ฅ+๏ŠซC
  • E143โˆš๐‘ฅ+๏ŠซC

Q18:

Determine ๏„ธ๐‘ฅ๏€น๐‘ฅ+2๏…๐‘ฅ๏Šจ๏Šจ๏Šจd.

  • A๐‘ฅ5+4๐‘ฅ3+4๐‘ฅ+๏Šซ๏ŠฉC
  • B๐‘ฅ6+๐‘ฅ+2๐‘ฅ+๏Šญ๏Šซ๏ŠฉC
  • C7๐‘ฅ+20๐‘ฅ+12๐‘ฅ+๏Šญ๏Šซ๏ŠฉC
  • D๐‘ฅ7+4๐‘ฅ5+4๐‘ฅ3+๏Šญ๏Šซ๏ŠฉC

Q19:

Determine ๏„ธ๏€ปโˆ’4โˆš๐‘ฅ+8๏‡โˆš๐‘ฅ๐‘ฅ๏Žค๏Žค๏Šฏ๏Šจd.

  • Aโˆ’5๐‘ฅ4+40๐‘ฅ7+๏Ž ๏Žฅ๏Žค๏Žฆ๏ŽคC
  • Bโˆ’64๐‘ฅ5+56๐‘ฅ5+๏Ž ๏Žฅ๏Žค๏Žฆ๏ŽคC
  • Cโˆ’72๐‘ฅ73+16๐‘ฅ7+๏Žฆ๏Žข๏Ž ๏Žง๏Žฆ๏ŽกC
  • Dโˆ’20๐‘ฅ11+20๐‘ฅ+๏Ž ๏Žฅ๏Žค๏Žฆ๏ŽคC

Q20:

Determine ๏„ธ๏€ฟ9โˆš๐‘ฅ+2๐‘ฅโˆ’1โˆš๐‘ฅ๏‹๐‘ฅd.

  • A12๏€ปโˆ’2โˆš๐‘ฅ+๐‘ฅ+6โˆš๐‘ฅ๏‡+๏Šจ๏Šฉ๏ŠจC
  • Bโˆ’โˆš๐‘ฅ+2๐‘ฅ+9โˆš๐‘ฅ+๏Šจ๏ŠฉC
  • Cโˆ’2โˆš๐‘ฅ+๐‘ฅ+6โˆš๐‘ฅ+๏Šจ๏ŠฉC
  • D8โˆš๐‘ฅ+๐‘ฅ+๏ŠจC

Q21:

Determine ๏„ธ๏€ป3โˆš๐‘ฅ+1๏‡๐‘ฅ๏Žข๏Šจ๏Šจd.

  • A10๐‘ฅ+36๐‘ฅ+๐‘ฅ+๏Žค๏Žก๏ŠชC
  • B12๐‘ฅ5+9๐‘ฅ4+๐‘ฅ+๏Žค๏Žก๏ŠชC
  • C4๐‘ฅ+3๐‘ฅ+๐‘ฅ+๏Žค๏Žก๏ŠชC
  • D27๐‘ฅ7+18๐‘ฅ5+๐‘ฅ+๏Žฆ๏Žข๏Žค๏ŽขC

Q22:

Determine ๏„ธ8โˆš๐‘ฅ๐‘ฅ๏Žค๏Šฌd.

  • A8๐‘ฅ+๏Šฑ๏Ž ๏ŽคC
  • Bโˆ’4011๐‘ฅ+๏Šฑ๏Ž ๏Ž ๏ŽคC
  • Cโˆ’85๐‘ฅ+๏Šฑ๏Ž ๏ŽคC
  • Dโˆ’203๐‘ฅ+๏Šฑ๏Ž ๏ŽคC
  • Eโˆ’40๐‘ฅ+๏Šฑ๏Ž ๏ŽคC

Q23:

Determine ๏„ธโˆš๐‘ฆโˆš๐‘ฆ๐‘ฆ๏Žค๏Žข๏Šจd.

  • A15๐‘ฆ+๏Ž ๏Žฅ๏Ž ๏ŽคC
  • B16๐‘ฆ15+๏Ž ๏Žฅ๏Ž ๏ŽคC
  • C15๐‘ฆ16+๏Ž ๏Žฅ๏Ž ๏ŽคC
  • Dโˆ’1514๐‘ฆ+๏Ž ๏Žฃ๏Ž ๏ŽคC

Q24:

Determine ๏„ธ๏€นโˆ’7๐‘ฅโˆ’5๏…๏€นโˆ’๐‘ฅ+1๏…๐‘ฅ๏Šจ๏Šฉd.

  • A7๐‘ฅ6+5๐‘ฅ4โˆ’7๐‘ฅ3โˆ’5๐‘ฅ+๏Šฌ๏Šช๏ŠฉC
  • B42๐‘ฅ+20๐‘ฅโˆ’21๐‘ฅโˆ’5๐‘ฅ+๏Šฌ๏Šช๏ŠฉC
  • C7๐‘ฅ4+5๐‘ฅ2โˆ’7๐‘ฅ+๏Šช๏ŠจC
  • D7๐‘ฅ5+5๐‘ฅ3โˆ’7๐‘ฅ2โˆ’5๐‘ฅ+๏Šฌ๏Šช๏ŠฉC

Q25:

Determine ๏„ธ๐‘ฅ+216๐‘ฅโˆ’6๐‘ฅ+36๐‘ฅ๏Šฉ๏Šจd.

  • A๐‘ฅ3โˆ’3๐‘ฅ+36๐‘ฅ+๏Šฉ๏ŠจC
  • B๐‘ฅ2โˆ’6๐‘ฅ+๏ŠจC
  • C๐‘ฅ4โˆ’216๐‘ฅ+๏ŠชC
  • D๐‘ฅ2+6๐‘ฅ+๏ŠจC

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