Alapintegrálok lineáris helyettesítései

\( \int (ax+b)^n \; dx = \frac{ (ax+b)^{n+1}}{n+1} \frac{1}{a}+c \)

\( \int \frac{1}{ax+b} \; dx = \ln{ \mid ax+b \mid}\frac{1}{a} + c \)

\( \int e^{ax+b} \; dx = e^{ax+b}\frac{1}{a} + c \)

\( \int A^{ax+b} \; dx = \frac{A^{ax+b}}{\ln{a}}\frac{1}{a} + c \)

\( \int \cos{(ax+b)} \; dx = \sin{(ax+b)}\frac{1}{a} + c \)

\( \int \sin{(ax+b)} \; dx = -\cos{(ax+b)}\frac{1}{a} + c \)

\( \int \frac{1}{\cos^2{(ax+b)} } \; dx = \tan{(ax+b)}\frac{1}{a} + c \)

\( \int \frac{1}{\sin^2{(ax+b)} } \; dx = - \cot{(ax+b)}\frac{1}{a} + c \)

\( \int \frac{1}{1+(ax+b)^2} \; dx = \arctan{(ax+b)}\frac{1}{a} + c \)