# Integration Formulas for Class 12 – Indefinite Integration

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!