প্রতিস্থাপন পদ্ধতি (Method of Substitution)
∫1x(1+Inx)dx \int \frac{1}{\mathrm{x}(1+\operatorname{In} \mathrm{x})} \mathrm{dx} ∫x(1+Inx)1dx এর মান কত ?
In(1+In(x)) \operatorname{In}(1+\operatorname{In}(x)) In(1+In(x))
In(x) \operatorname{In}(\mathrm{x}) In(x)
x3 x^{3} x3
0
I=∫1x(1+lnx)dx=∫dzz=lnz+c=ln(1+lnx)+c I=\int \frac{1}{x(1+\ln x)} d x=\int \frac{d z}{z}=\ln z+c=\ln (1+\ln x)+c I=∫x(1+lnx)1dx=∫zdz=lnz+c=ln(1+lnx)+c
∫ex(x+1)dxsin2(xex)=? \int \frac{e^{x} \left ( x + 1 \right ) dx}{\sin^{2}{\left ( x e^{x} \right )}} = ? ∫sin2(xex)ex(x+1)dx=?
∫exdx1+e2x=f(x)+c \int \frac{e^{x} dx}{1 + e^{2 x}} = f{\left ( x \right )} + c ∫1+e2xexdx=f(x)+c
হলে, f(x)=?
What is ∫x4−1x2x4+x2+1dx\displaystyle \int \dfrac{x^4 - 1}{x^2 \sqrt{x^4 + x^2 + 1}} dx∫x2x4+x2+1x4−1dx equal to?
∫sinx3+4cosxdx=?\int \frac{\sin x}{3+4 \cos x} d x = ?∫3+4cosxsinxdx=?
