Pertanyaan

∫ sec 3 x d x = …

$\int sec^{3} x d x = \dots$

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$s e c 3 space x space equals space s e c space x space. space s e c 2 space x integral sec cubed invisible function application x d x equals integral sec invisible function application x. sec squared invisible function application x d x G u n a k a n space i n t e g r a l space p a r s i a l comma space m i s a l k a n space u equals sec invisible function application x rightwards arrow fraction numerator d u over denominator d x end fraction equals sec invisible function application x tan invisible function application x rightwards arrow d u equals sec invisible function application x tan invisible function application x space d x d v equals sec squared invisible function application x rightwards arrow v equals integral sec squared invisible function application x d x equals tan invisible function application x I n g a t space r u m u s space i n t e g r a l space p a r s i a l space integral u d v equals u v minus integral v d u integral sec cubed invisible function application x d x equals sec invisible function application x t a n x minus integral tan invisible function application x. sec invisible function application x. tan invisible function application x d x integral sec cubed invisible function application x d x equals sec invisible function application x t a n x minus integral tan squared invisible function application x. sec invisible function application x d x integral sec cubed invisible function application x d x equals sec invisible function application x t a n x minus integral open parentheses sec squared invisible function application x minus 1 close parentheses. sec invisible function application x d x integral sec cubed invisible function application x d x equals sec invisible function application x t a n x minus integral open parentheses sec cubed invisible function application x minus sec invisible function application x close parentheses space d x integral sec cubed invisible function application x d x equals sec invisible function application x t a n x minus integral sec cubed invisible function application x space d x plus integral sec invisible function application x d x 2 integral sec cubed invisible function application x d x equals s e c x tan invisible function application x space plus integral sec invisible function application x d x 2 integral sec cubed invisible function application x d x equals s e c x tan invisible function application x space plus ln invisible function application open vertical bar sec invisible function application x plus tan invisible function application x close vertical bar plus C integral sec cubed invisible function application x d x equals 1 half s e c x tan invisible function application x space plus 1 half ln invisible function application open vertical bar sec invisible function application x plus tan invisible function application x close vertical bar plus C$