Hasil dari ∫cscxdx=...

Pertanyaan

Hasil dari begin mathsize 14px style integral csc invisible function application x d x equals... end style

  1. begin mathsize 14px style negative ln invisible function application open vertical bar csc invisible function application x plus cot invisible function application x close vertical bar plus C end style

  2. begin mathsize 14px style negative ln invisible function application open vertical bar cscc invisible function application x plus sec invisible function application x close vertical bar plus C end style

  3. begin mathsize 14px style negative ln invisible function application open vertical bar sec invisible function application x plus tan invisible function application x close vertical bar plus C end style

  4. begin mathsize 14px style ln invisible function application open vertical bar cos invisible function application x plus sin invisible function application x close vertical bar plus C end style

  5. begin mathsize 14px style ln invisible function application open vertical bar csc invisible function application x plus cot invisible function application x close vertical bar plus C end style

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Pembahasan

Agar dapat menggunakan integral subsitusi perlu kita kalikan dengan

begin mathsize 14px style fraction numerator csc invisible function application x plus cot invisible function application x over denominator csc invisible function application x plus cot invisible function application x end fraction end style 

Sehingga fungsi tersebut menjadi,

begin mathsize 14px style integral csc invisible function application x d x equals integral open parentheses csc invisible function application x times fraction numerator csc invisible function application x plus cot invisible function application x over denominator csc invisible function application x plus cot invisible function application x end fraction close parentheses d x space space space space space space space space space space space space space space space space space space space equals integral open parentheses fraction numerator csc squared invisible function application x plus csc invisible function application x cot invisible function application x over denominator csc invisible function application x plus cot invisible function application x end fraction close parentheses d x end style 

Kemudian kita gunakan integral substitusi dengan memisalkan begin mathsize 14px style u equals csc invisible function application x plus cot invisible function application x end style sehingga diperoleh,

begin mathsize 14px style fraction numerator d u over denominator d x end fraction equals csc invisible function application x plus cot invisible function application x d x equals fraction numerator d u over denominator negative csc invisible function application x cot invisible function application x plus cosec squared invisible function application x end fraction end style

 

Maka,

begin mathsize 14px style integral csc invisible function application x d x equals integral open parentheses csc invisible function application x times fraction numerator csc invisible function application x plus cot invisible function application x over denominator csc invisible function application x plus cot invisible function application x end fraction close parentheses d x space space space space space space space space space space space space space space space space space space space equals integral open parentheses fraction numerator csc squared invisible function application x plus csc invisible function application x cot invisible function application x over denominator csc invisible function application x plus cot invisible function application x end fraction close parentheses d x space space space space space space space space space space space space space space space space space space space equals integral open parentheses fraction numerator csc squared invisible function application x plus csc invisible function application x cot invisible function application x over denominator u end fraction close parentheses times fraction numerator d u over denominator negative csc invisible function application x cot invisible function application x plus csc squared invisible function application x end fraction space space space space space space space space space space space space space space space space space space space equals integral negative 1 over u d u space space space space space space space space space space space space space space space space space space space equals negative ln invisible function application u plus C space space space space space space space space space space space space space space space space space space space equals negative ln invisible function application open vertical bar csc invisible function application x plus cot invisible function application x close vertical bar plus C end style 

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