Inicio/Cálculo II/Apéndice A: tabla extensa de antiderivadas/A.3. Integrales trigonométricas inversasContenidoA.3. Integrales trigonométricas inversasA.3.1 Integrales directasCopiar LaTeX∫arcsenu du=u arcsenu+1−u2+C\int \operatorname{arcsen} u\,du = u\,\operatorname{arcsen} u + \sqrt{1 - u^2} + C∫arcsenudu=uarcsenu+1−u2+CVer detalle →FórmulaCopiar LaTeX∫arccosu du=u arccosu−1−u2+C\int \arccos u\,du = u\,\arccos u - \sqrt{1 - u^2} + C∫arccosudu=uarccosu−1−u2+CVer detalle →FórmulaCopiar LaTeX∫arctanu du=u arctanu−12 ln(1+u2)+C\int \arctan u\,du = u\,\arctan u - \frac{1}{2}\,\ln\left(1 + u^2\right) + C∫arctanudu=uarctanu−21ln(1+u2)+Cln(1+u2)+C\ln\left(1 + u^2\right) + Cln(1+u2)+CVer detalle →A.3.2 Producto con uuuCopiar LaTeX∫u arcsenu du=2u2−14 arcsenu+u1−u24+C\int u\,\operatorname{arcsen} u\,du = \frac{2u^2 - 1}{4}\,\operatorname{arcsen} u + \frac{u\sqrt{1 - u^2}}{4} + C∫uarcsenudu=42u2−1arcsenu+4u1−u2+CVer detalle →FórmulaCopiar LaTeX∫u arctanu du=u2+12 arctanu−u2+C\int u\,\arctan u\,du = \frac{u^2 + 1}{2}\,\arctan u - \frac{u}{2} + C∫uarctanudu=2u2+1arctanu−2u+CVer detalle →A.3.3 Potencias generales (n≠−1n \neq -1n=−1)Copiar LaTeX∫un arcsenu du=1n+1[un+1 arcsenu−∫un+1 du1−u2]\int u^n\,\operatorname{arcsen} u\,du = \frac{1}{n+1}\left[u^{n+1}\,\operatorname{arcsen} u - \int \frac{u^{n+1}\,du}{\sqrt{1 - u^2}}\right]∫unarcsenudu=n+11[un+1arcsenu−∫1−u2un+1du]Ver detalle →FórmulaCopiar LaTeX∫un arccosu du=1n+1[un+1 arccosu+∫un+1 du1−u2]\int u^n\,\arccos u\,du = \frac{1}{n+1}\left[u^{n+1}\,\arccos u + \int \frac{u^{n+1}\,du}{\sqrt{1 - u^2}}\right]∫unarccosudu=n+11[un+1arccosu+∫1−u2un+1du]Ver detalle →FórmulaCopiar LaTeX∫un arctanu du=1n+1[un+1 arctanu−∫un+1 du1+u2]\int u^n\,\arctan u\,du = \frac{1}{n+1}\left[u^{n+1}\,\arctan u - \int \frac{u^{n+1}\,du}{1 + u^2}\right]∫unarctanudu=n+11[un+1arctanu−∫1+u2un+1du]Ver detalle →
A.3.1 Integrales directasCopiar LaTeX∫arcsenu du=u arcsenu+1−u2+C\int \operatorname{arcsen} u\,du = u\,\operatorname{arcsen} u + \sqrt{1 - u^2} + C∫arcsenudu=uarcsenu+1−u2+CVer detalle →
FórmulaCopiar LaTeX∫arccosu du=u arccosu−1−u2+C\int \arccos u\,du = u\,\arccos u - \sqrt{1 - u^2} + C∫arccosudu=uarccosu−1−u2+CVer detalle →
FórmulaCopiar LaTeX∫arctanu du=u arctanu−12 ln(1+u2)+C\int \arctan u\,du = u\,\arctan u - \frac{1}{2}\,\ln\left(1 + u^2\right) + C∫arctanudu=uarctanu−21ln(1+u2)+Cln(1+u2)+C\ln\left(1 + u^2\right) + Cln(1+u2)+CVer detalle →
A.3.2 Producto con uuuCopiar LaTeX∫u arcsenu du=2u2−14 arcsenu+u1−u24+C\int u\,\operatorname{arcsen} u\,du = \frac{2u^2 - 1}{4}\,\operatorname{arcsen} u + \frac{u\sqrt{1 - u^2}}{4} + C∫uarcsenudu=42u2−1arcsenu+4u1−u2+CVer detalle →
FórmulaCopiar LaTeX∫u arctanu du=u2+12 arctanu−u2+C\int u\,\arctan u\,du = \frac{u^2 + 1}{2}\,\arctan u - \frac{u}{2} + C∫uarctanudu=2u2+1arctanu−2u+CVer detalle →
A.3.3 Potencias generales (n≠−1n \neq -1n=−1)Copiar LaTeX∫un arcsenu du=1n+1[un+1 arcsenu−∫un+1 du1−u2]\int u^n\,\operatorname{arcsen} u\,du = \frac{1}{n+1}\left[u^{n+1}\,\operatorname{arcsen} u - \int \frac{u^{n+1}\,du}{\sqrt{1 - u^2}}\right]∫unarcsenudu=n+11[un+1arcsenu−∫1−u2un+1du]Ver detalle →
FórmulaCopiar LaTeX∫un arccosu du=1n+1[un+1 arccosu+∫un+1 du1−u2]\int u^n\,\arccos u\,du = \frac{1}{n+1}\left[u^{n+1}\,\arccos u + \int \frac{u^{n+1}\,du}{\sqrt{1 - u^2}}\right]∫unarccosudu=n+11[un+1arccosu+∫1−u2un+1du]Ver detalle →
FórmulaCopiar LaTeX∫un arctanu du=1n+1[un+1 arctanu−∫un+1 du1+u2]\int u^n\,\arctan u\,du = \frac{1}{n+1}\left[u^{n+1}\,\arctan u - \int \frac{u^{n+1}\,du}{1 + u^2}\right]∫unarctanudu=n+11[un+1arctanu−∫1+u2un+1du]Ver detalle →