intigration of Rational Algebraic Fractions (মূলদ ভগ্নাংশ)
∫dxxlnxএরমানকত? \int \frac{dx}{x \ln{x}} এ র ম া ন ক ত ? ∫xlnxdxএরমানকত?
ln(lnx)
ln(1/X)
ln(lnx)+c
None of them
lnx=z⇒1xdx=dz;∫dzz=lnz=ln(lnx)+c \ln \mathrm{x}=\mathrm{z} \Rightarrow \frac{1}{\mathrm{x}} \mathrm{dx}=\mathrm{dz} ; \int \frac{\mathrm{dz}}{\mathrm{z}}=\ln \mathrm{z}=\ln (\ln \mathrm{x})+\mathrm{c} lnx=z⇒x1dx=dz;∫zdz=lnz=ln(lnx)+c formula: ∫f′(x)f(x)dx=ln{f(x)}+c \int \frac{f^{\prime}(x)}{f(x)} d x=\ln \{f(x)\}+c \quad ∫f(x)f′(x)dx=ln{f(x)}+c
∫x2+x+1x2−x+1dx \int \frac{x^{2}+x+1}{x^{2}-x+1} d x ∫x2−x+1x2+x+1dx
P=(x−4)2(x−3) P=(x-4)^{2}(x-3) P=(x−4)2(x−3) এবং g(x,y)=x2+y2 g(x, y)=x^{2}+y^{2} g(x,y)=x2+y2
∫1ex+1dx=?\int \frac{1}{e^{x}+1} d x = ?∫ex+11dx=?
দৃশ্যকল্প: g(x)=cot−1x,f(x)=x g(x)=\cot ^{-1}x, f(x)=x g(x)=cot−1x,f(x)=x
P=(x−4)2(x−3) P=(x-4)^{2}(x-3) P=(x−4)2(x−3)
