বিভিন্ন সূত্রের ব্যবহারে যোগজীকরণ
∫4x31+x8dx=f(x)+c \int \frac{4 x ³}{1 + x^{8}} dx = f{\left ( x \right )} + c ∫1+x84x3dx=f(x)+c হলে f(x) এর মান কত?
11+x2 \frac{1}{1 + x^{2}} 1+x21
sin−1x3 \sin^{- 1}{x} ³ sin−1x3
tan−1x4 \tan^{- 1}{x} ⁴ tan−1x4
tan−1x3 \tan^{- 1}{x} ³ tan−1x3
∫4x31+x8dx \int \frac{4 x^{3}}{1+x^{8}} d x ∫1+x84x3dx
∫cos2x°dx= \int \cos{2} x ° dx = ∫cos2x°dx= কত?
∫dxxx2−1=f(x)+c \int \frac{dx}{x \sqrt{x^{2} - 1}} = f{\left ( x \right )} + c ∫xx2−1dx=f(x)+c
হলে, f(x)=?
f(x)=a2+x2 হলে-
∫dxf(x)=1atan−1(xa)+c \int \frac{dx}{f{\left ( x \right )}} = \frac{1}{a} \tan^{- 1}{\left ( \frac{x}{a} \right )} + c ∫f(x)dx=a1tan−1(ax)+c
∫dxf(x)=ln∣x+x2+a2∣+c \int \frac{dx}{\sqrt{f{\left ( x \right )}}} = \ln{\left \lvert x + \sqrt{x^{2} + a^{2}} \right \rvert} + c ∫f(x)dx=lnx+x2+a2+c
∫dx{f(x)}3=xa2(x2+a2)+c \int \frac{dx}{\sqrt{\left \lbrace f{\left ( x \right )} \right \rbrace}^{3}} = \frac{x}{a^{2} \left ( \sqrt{x^{2} + a^{2}} \right )} + c ∫{f(x)}3dx=a2(x2+a2)x+c
নিচের কোনটি সঠিক?
∫01sin−1x1−x2dx \int_{0}^{1} \frac{\sin ^{-1} x}{\sqrt{1-x^{2}}} \mathrm{dx} ∫011−x2sin−1xdx এর মান কত?
