Here you will learn Integration integration formulas for class 12.
Let’s begin –
Integration Formula for Class 12
(i) \(\int\) \({(ax+b)}^n\) dx = \({(ax+b)}^{n+1}\over {a(n+1)}\) + C ; n \(\ne\) -1
(ii) \(\int\) \(dx\over {ax+b}\) dx = \(1\over a\) ln|ax+b| + C
(iii) \(\int\) \(e^{ax+b}\) dx = \({1\over {a}}e^{ax+b}\) + C or \(\int\) \(e^x\) = \(e^x\) + C
(iv) \(\int\) \(a^{px+q}\) dx = \({1\over p}\) \({a^{px+q}}\over lna\) + C, (a > 0)
(v) \(\int\) sinx dx = -cosx + C
(vi) \(\int\) cosx dx = sinx + C
(vii) \(\int\) tanx dx = ln|secx| + C
(viii) \(\int\) cotx dx = ln|sinx| + C
(ix) \(\int\) \(sec^2x\) dx = tanx + C
(x) \(\int\) \(cosec^2x\) dx = -cotx + C
(xi) \(\int\) cosecx.cotx dx = -cosecx + C
(xii) \(\int\) secx.tanx dx = secx + C
(xiii) \(\int\) secx dx = ln|secx+tanx| + C = ln|tan(\(\pi\over 4\) + \(x\over 2\))| + C
(xiv) \(\int\) cosecx dx = ln|cosecx-cotx| + C = ln|tan\(x\over 2\)| = -ln|cosecx+cotx| + C
(xv) \(\int\) \(dx\over {\sqrt{a^2-x^2}}\) = \(sin^{-1} {x\over a}\) + C
(xvi) \(\int\) \(dx\over {a^2+x^2}\) = \(1\over a\) \(tan^{-1} {x\over a}\) + C
(xvii) \(\int\) \(dx\over {x\sqrt{x^2-a^2}}\) = \(1\over a\) \(sec^{-1} {x\over a}\) + C
(xviii) \(\int\) \(dx\over {\sqrt{x^2+a^2}}\) = \(ln[x+\sqrt{x^2+a^2}]\) + C
(xix) \(\int\) \(dx\over {\sqrt{x^2-a^2}}\) = \(ln[x+\sqrt{x^2-a^2}]\) + C
(xx) \(\int\) \(dx\over {a^2-x^2}\) = \(1\over 2a\) \(ln|{a+x\over {a-x}}|\) + C
(xxi) \(\int\) \(dx\over {x^2-a^2}\) = \(1\over 2a\) \(ln|{x-a\over {x+a}}|\) + C
(xxii) \(\int\) \(\sqrt{a^2-x^2}\) dx = \(x\over 2\)\(\sqrt{a^2-x^2}\) + \(a^2\over 2\) \(sin^{-1} {x\over a}\) + C
(xxii) \(\int\) \(\sqrt{x^2+a^2}\) dx = \(x\over 2\)\(\sqrt{x^2+a^2}\) + \(a^2\over 2\) \(ln[x+\sqrt{x^2+a^2}]\) + C
(xxii) \(\int\) \(\sqrt{x^2-a^2}\) dx = \(x\over 2\)\(\sqrt{x^2-a^2}\) – \(a^2\over 2\) \(ln[x+\sqrt{x^2-a^2}]\) + C
Hope you learnt integration formulas for class 12, learn more concepts of integration and practice more questions to get ahead in competition. Good Luck!
