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∫ sec 3 x d x = ...

  1. 1 half s e c space x space tan space x plus 1 half ln open vertical bar s e c space x space plus space tan space x close vertical bar plus C

  2. 1 half s e c space x space tan space x minus 1 half ln open vertical bar s e c space x space plus space tan space x close vertical bar plus C

  3. negative 1 half s e c x space tan space x plus 1 half ln open vertical bar s e c space x space plus space tan space x close vertical bar plus C

  4. s e c space x space tan space x plus ln open vertical bar s e c space x space plus thin space tan space x close vertical bar plus C

  5. s e c space x space tan space x minus ln open vertical bar s e c space x space plus thin space tan space x close vertical bar plus C

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R. RGFLSATU

Master Teacher

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Pembahasan

sec 3 x dx = sec x . sec 2 x dx sec 3 x dx = sec x . sec 2 x dx Gunakan integral parsial, misalkan Ingat rumus integral parsial

s e c cubed space x space equals space s e c space x space. space s e c squared space x

integral sec cubed x space d x equals integral sec space x. sec squared x space d x

Gunakan integral parsial, misalkan u equals sec space x rightwards arrow fraction numerator d u over denominator d x end fraction equals sec space x space tan space x rightwards arrow d u equals sec space x space tan space x space d x

d v equals s e c squared x rightwards arrow v equals integral sec squared x space d x equals tan space x

Ingat rumus integral parsial integral u d v equals u v minus integral v d u

integral sec cubed x space d x equals sec space x space tan space x minus integral tan space x. sec space x. space tan space x space d x integral sec cubed x space d x equals sec space x space tan space x minus integral tan squared x. sec space x space d x integral sec cubed x space d x equals sec space x space tan space x minus integral left parenthesis sec squared x minus 1 right parenthesis. sec space x space d x integral sec cubed x space d x equals sec space x space tan space x minus integral left parenthesis sec cubed x minus sec space x right parenthesis space d x integral sec cubed x space d x equals sec space x space tan space x minus integral sec cubed x space d x plus integral sec space x space d x 2 integral sec cubed x space d x equals sec space x space tan space x space plus space integral sec space x space d x 2 space integral sec cubed x space d x equals sec space x space tan space x space plus space ln open vertical bar sec space x space plus tan space x close vertical bar plus C integral sec cubed x space d x equals 1 half sec space x space tan space x space plus 1 half ln open vertical bar sec space x space plus space tan space x close vertical bar plus C

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