Integrales Inmediatas

Tabla de Integrales Inmediatas

Integral de una Constante	\(\displaystyle \int k \; dx = k\cdot x + C\)
Integral de x	\(\displaystyle \int x \; dx = \frac{1}{2}x^2 + C\)
Integral de Potencia de x	\(\displaystyle \int x^k \; dx = \frac{1}{k+1}x^{k+1} + C\) (k ≠ -1).
Integral de 1/x	\(\displaystyle \int \frac{1}{x} \; dx = \ln x + C\)
Integral de Exponencial	\(\displaystyle \int a^x \; dx = \frac{a^x}{\ln a} + C\)
Integral de Exponencial de base e	\(\displaystyle \int e^x \; dx = e^x + C\)
Integral del Logaritmo Neperiano	\(\displaystyle \int \ln x \; dx = x\ln(x) -x + C\)
Integral del Logaritmo	\(\displaystyle \int \log_a x \; dx = \int \frac{\ln x}{\ln a} \; dx = \frac{x\ln(x) -x}{\ln a} + C\)
Integral del Seno	\(\displaystyle \int sen(x) \; dx = -cos(x) + C\)
Integral del Coseno	\(\displaystyle \int cos(x) \; dx = sen(x) + C\)
Integral de la Tangente	\(\displaystyle \int tan(x) \; dx = -\ln{|cos(x)|} + C\)
Integral de la Cosecante	\(\displaystyle \int cosec(x) \; dx = -\ln{|cosec(x) + cotg(x)|} + C\)
Integral de la Secante	\(\displaystyle \int sec(x) \; dx = \ln{|sec(x) + tan(x)|} + C\)
Integral de la Cotangente	\(\displaystyle \int sec(x) \; dx = \ln{|sen(x)|} + C\)
Integral del Arcoseno	\(\displaystyle \int arcsen(x) \; dx = \frac{1}{\sqrt{1-x^2}} + C\)
Integral del Arcocoseno	\(\displaystyle \int arcsen(x) \; dx = \frac{-1}{\sqrt{1-x^2}} + C\)
Integral del Arcotangente	\(\displaystyle \int arctan(x) \; dx = \frac{1}{1+x^2} + C\)
Integral del Arcocotangente	\(\displaystyle \int arccotan(x) \; dx = \frac{-1}{1+x^2} + C\)
Integral del Arcosecante	\(\displaystyle \int arcsen(x) \; dx = \frac{1}{|x|\sqrt{1-x^2}} + C\)
Integral del Arcocosecante	\(\displaystyle \int arcsen(x) \; dx = \frac{-1}{|x|\sqrt{1-x^2}} + C\)