Fórmulas Básicas

$$\int udv = uv - \int vdu$$

$$\int u^n du = \frac{u^{n+1}}{n+1}+C \hspace{2em} (n \neq 1)$$

$$\int \frac{du}{u} = ln|u|+C$$

$$\int e^u du = e^u + C$$

$$\int a^u du = \frac{a^u}{lna}+C$$

$$\int sin \: u \: du = -cos \: u+C$$

$$\int cos \: u \: du = sin \: u+C$$

$$\int sec^2 u \: du = tan \: u+C$$

$$\int csc^2 u \: du = -cot \: u+C$$

$$\int sec\: u \: tan \: u \: du = sec \: u+C$$

$$\int csc\: u \: cot \: u \: du = -csc \: u+C$$

$$\int tan \: u \: du = ln|sec \: u| \: +C$$

$$\int cot \: u \: du = ln|sin \: u| \: +C$$

$$\int sec \: u \: du = ln|sec \: u + tan \: u| \: +C$$

$$\int csc \: u \: du = ln|csc \: u - cot \: u| \: +C$$

$$\int \frac{du}{\sqrt{a^2 - u^2}} = sin^{-1} (\frac{u}{a}) + C$$

$$\int \frac{du}{\sqrt{a^2 + u^2}} = \frac{1}{a} \: tan^{-1} (\frac{u}{a}) + C$$

$$\int \frac{du}{u \sqrt{u^2 - a^2}} = \frac{1}{a} \: sec^{-1} (\frac{u}{a}) + C$$

$$\int \frac{du}{a^2 - u^2} = \frac{1}{2a} \: ln|\frac{u+a}{u-a}| + C$$

$$\int \frac{du}{u^2 - a^2} = \frac{1}{2a} \: ln|\frac{u-a}{u+a}| + C$$