INTEGRATION FORMULA LIST

Integration is the important part of class XII mathematics.The weightage of Integration in Class XII board exams is about 20 marks.Here is the detailed Formula list for Integration......

CBSE Class 12 Maths Sample Paper 2018 with Solution $$\begin{array}{l}1.{\displaystyle \int x^{n}dx=\left(\frac{x^{n+1}}{n+1}\right)+c,n\ne -1}\\ 2.{\displaystyle \int \left[f\left(x\right)+g\left(x\right)+h\left(x\right)\right]dx={\displaystyle \int f\left(x\right)dx+{\displaystyle \int g\left(x\right)dx+{\displaystyle \int h\left(x\right)dx+c}}}}\\ 3.{\displaystyle \int a{x}^{n}dx=a\left(\frac{x^{n+1}}{n+1}\right)+c,n\ne -1}\\ 4.{\displaystyle \int kdx=kx+c}\\ 5.{\displaystyle \int {\left(ax+b\right)}^{n}dx=\frac{{\left(ax+b\right)}^{n+1}}{a\left(n+1\right)}+c,n\ne -1}\\ 6.{\displaystyle \int \frac{dx}{x^n}=\frac{-1}{\left(n+1\right)x^{n-1}}+c,n\ne -1}\\ 7.{\displaystyle \int \frac{dx}{{\left(ax+b\right)}^n}=\frac{-1}{a\left(n-1\right){\left(ax+b\right)}^{n-1}}+c,}n\ne -1\\ 8.{\displaystyle \int \frac{dx}{x}=\log \left|x\right|+c}\\ 9.{\displaystyle \int \frac{dx}{ax+b}=\frac{1}{a}\log |ax+b|+c}\\ 10.{\displaystyle \int \frac{dx}{\sqrt{\left(ax+b\right)}}=\frac{2\sqrt{\left(ax+b\right)}}{a}+c}\\ 11.{\displaystyle \int e^{x}dx=e^x}\\ 12.{\displaystyle \int e^{ax+b}dx=\frac{e^{ax+b}}{a}+c}\\ 13.{\displaystyle \int a^{x}dx=\frac{a^x}{\log a}+c}\\ 14.{\displaystyle \int a^{mx+n}dx=\frac{a^{mx+n}}{m\log a}+c}\\ 15.{\displaystyle \int \sin xdx=-\cos x+c}\\ 16.{\displaystyle \int \cos xdx=\sin x+c}\\ 17.{\displaystyle \int \tan xdx=-\log |\cos x|+c=\log |\sec x|+c}\\ 18.{\displaystyle \int \cot xdx=\log |\sin x|+c=-\log |\cos ecx|+c}\\ 19.{\displaystyle \int \sec xdx=\log |\sec x+\tan x|+c=\log \left|\tan \left(\frac{\pi }{4}+\frac{x}{2}\right)\right|+c }\end{array}$$

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