integral of houphd

$$int kdx = kx+C\ int x^{mu }dx=frac{x^{mu +1}}{mu +1}+C)(mu notequiv -1)\ int a^{x}dx=frac{1}{lna}a^{x}+C\ int e^{x}dx=e^{x}+C\ int sinxdx=-cosx+C\ int cosxdx=sinx+C\ int frac{dx}{x}=lnleft | x right |+C(xneq 0)\ int tanxdx=-lnleft | cosx right |+C\ int cotxdx=lnleft | sinx right |+C\ int frac{1}{cosx}dx=lnleft | frac{1}{cosx} +tanx right |+C\ int frac{1}{sinx}dx=lnleft | frac{1}{sinx}-cotx right |+C\ int frac{1}{cos^{2}x}dx=tanx+C\ int frac{1}{sin^{2}x}dx=-cosx+C\ int frac{sinx}{cos^{2}x}dx=frac{1}{cosx}+C\ int frac{cosx}{sin^{2}x}dx=-frac{1}{sinx}+C\ int frac{1}{sqrt{a^{2}-x^{2}}}dx=arcsinfrac{x}{a}+C\ int frac{1}{a^{2}+x^{2}}dx=frac{1}{a}arctanfrac{x}{a}+C\ int frac{1}{x^{2}-a^{2}}dx=frac{1}{2a}lnleft | frac{x-a}{x+a} right |+C\ int frac{1}{a^{2}-x^{2}}dx=frac{1}{2a}lnleft | frac{a+x}{a-x} right |+C\ int frac{1}{sqrt{x^{2}pm a^{2}}}dx=lnleft | x+sqrt{x^{2}pm a^{2}} right |+C$$