Last active
March 7, 2023 22:16
-
-
Save thinkphp/c0d9b4aa350d7db8ed6d28af364a86c6 to your computer and use it in GitHub Desktop.
Integrals
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
$\int{f(x) g'(x) \ dx} = fg - \int{ g(x) f'(x) \ dx}$ | |
$\int{cos^2x \ dx} = \int{cos \ x \ cos \ x \ dx} = \int{cos \ x \ (sin \ x)' \ dx} = cos \ x \ sin \ x - \int{sin \ x \ (cos \ x)' \ dx} = cos \ x \ sin \ x - \int{sin \ x \ sin \ x \ dx} = cos \ x \ sin \ x - \int{sin^2 \ x \ dx} = sin\ x \ cos \ x + \int{sin^2 \ x \ dx} = sin\ x \ cos \ x + \int{ (1 - cos^2 \ x) \ x \ dx} = sin\ x \ cos \ x + \int{ 1 \ dx} - \int{ cos^2 \ x \ dx} = sin\ x \ cos \ x + x - \int{ cos^2 \ x \ dx} => \int \cos ^2x\,dx=\frac{x+\sin x\cos x}{2}+C. $ |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment