7.1 Integration By Parts/33: Difference between revisions
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<math>\int(cos\sqrt{x})dx </math> = <math>2\sqrt{x}\int(cosu)du</math> = <math>2\int{u}(cosu)du</math> = <math>{2u}(sinu)-{2}\int(sinu)du</math> = <math>{2}\sqrt{x}(sin\sqrt{x})-(-2cosu)</math> = <math>{2}\sqrt{x}(sin\sqrt{x})+(2cos\sqrt{x})+{c} </math> | <math>\int(cos\sqrt{x})dx </math> = <math>2\sqrt{x}\int(cosu)du</math> | ||
= <math>2\int{u}(cosu)du</math> = <math>{2u}(sinu)-{2}\int(sinu)du</math> = <math>{2}\sqrt{x}(sin\sqrt{x})-(-2cosu)</math> = <math>{2}\sqrt{x}(sin\sqrt{x})+(2cos\sqrt{x})+{c} </math> | |||
<math>{u}</math> = <math>\sqrt{x}</math> | <math>{u}</math> = <math>\sqrt{x}</math> | ||
<math>{du}</math> = <math>\frac{1}{2\sqrt{x}}dx</math> | <math>{du}</math> = <math>\frac{1}{2\sqrt{x}}dx</math> | ||
<math>2\sqrt{x}{du}</math> = <math>{dx}</math> | <math>2\sqrt{x}{du}</math> = <math>{dx}</math> | ||
<math>{u}</math> = <math>{u}</math> , <math>{dv}</math> = <math>{cosu}du</math> | |||
<math>{du}</math> = <math>{du}</math> , <math>{v}</math> = <math>{sinu}</math> | |||
Latest revision as of 03:08, 23 November 2022
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