Question
Download Solution PDF\(\rm \int{dx\over\sqrt{(x+1)(x+2)}}\) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
समाकल गुण:
- ∫ xn dx = \(\rm x^{n+1}\over n+1\)+ C ; n ≠ -1
- \(\rm∫ {1\over x} dx = \ln x\) + C
- ∫ ex dx = ex+ C
- \(\rm \int{1\over\sqrt{x^2+a^2}}dx=\rm \ln|\sqrt{x^2 + a^2}+x| +c \)
गणना:
I = \(\rm \int{dx\over\sqrt{(x+1)(x+2)}}\)
माना कि u2 = x + 1 है।
⇒ 2u du = dx
I = \(\rm \int{2u\over u\sqrt{(u^2+1)}}du\)
I = \(\rm 2\int{1\over\sqrt{u^2+1}}du\)
I = \(\rm 2\ln|\sqrt{u^2 + 1}+u| +c \)
I = \(\rm 2\ln|\sqrt{x+1 + 1}+\sqrt{x+1}| +c \)
I = \(\boldsymbol{\rm 2\ln|\sqrt{x+2}+\sqrt{x+1}| +c } \)
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