প্রতিস্থাপন পদ্ধতি (Method of Substitution)
যোগজীকরণ কর।
∫cosx3+cos2xdx \int \frac{\cos x}{3+\cos ^{2} x} d x ∫3+cos2xcosxdx
3+cos2x=3+1−sin2x=22−sin2x 3+\cos ^{2} x=3+1-\sin ^{2} x=2^{2}-\sin ^{2} x 3+cos2x=3+1−sin2x=22−sin2x
ধরি,
u=sinx⇒du=cosdx∫cosx22−sin2xdx=∫122−u2du=14log∣2+sinx2−sinx∣+c \begin{array}{l} \mathrm{u}=\sin \mathrm{x}\Rightarrow \mathrm{du}=\cos \mathrm{dx} \\ \int \frac{\cos x}{2^{2}-\sin ^{2} x} d x=\int \frac{1}{2^{2}-u^{2}} d u \\ \quad=\frac{1}{4} \log \left|\frac{2+\sin x}{2-\sin x}\right|+c \end{array} u=sinx⇒du=cosdx∫22−sin2xcosxdx=∫22−u21du=41log2−sinx2+sinx+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)=?
∫ecos−1x1−x2dx \int \frac{e^{\cos^{- 1}{x}}}{\sqrt{1 - x ²}} dx ∫1−x2ecos−1xdx এর মান কত?
∫x2x3+1dx= \int \frac{x^{2}}{\sqrt{x^{3} + 1}} dx = ∫x3+1x2dx= কোনটি ?
∫dx(ex+e−x)2= \int \frac{dx}{\left ( e^{x} + e^{- x} \right )^{2}} = ∫(ex+e−x)2dx= কত?
