প্রতিস্থাপন পদ্ধতি (Method of Substitution)
∫x2cosx3dx=?\int x^{2} \cos x^{3} d x = ?∫x2cosx3dx=?
13sin2x2+c\frac{1}{3} \sin 2 x^{2}+c31sin2x2+c
13sin3x3+c\frac{1}{3} \sin 3 x^{3}+c31sin3x3+c
13sinx3+c\frac{1}{3} \sin x^{3}+c31sinx3+c
13sinx2+c\frac{1}{3} \sin x^{2}+c31sinx2+c
Solve:
∫x2cosx3dx=13∫cos(x3)(3x2dx)=13sinx3+c \begin{array}{l} \int x^{2} \cos x^{3} d x=\frac{1}{3} \int \cos \left(x^{3}\right)\left(3 x^{2} d x\right) \\ =\frac{1}{3} \sin x^{3}+c \end{array} ∫x2cosx3dx=31∫cos(x3)(3x2dx)=31sinx3+c
∫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=?
∫dxx1+lnx=?\int \frac{d x}{x \sqrt{1+\ln x}} = ?∫x1+lnxdx=?
