বিভিন্ন সূত্রের ব্যবহারে যোগজীকরণ
∫xdxx4+1=? \int \frac{x d x}{x^{4}+1} = ? ∫x4+1xdx=?
12⋅tan−1(x2)+c\frac{1}{2} \cdot \tan ^{-1}\left(x^{2}\right)+c21⋅tan−1(x2)+c
−12⋅tan−1(x2)+c-\frac{1}{2} \cdot \tan ^{-1}\left(x^{2}\right)+c−21⋅tan−1(x2)+c
14⋅tan−1(x2)+c\frac{1}{4} \cdot \tan ^{-1}\left(x^{2}\right)+c41⋅tan−1(x2)+c
12⋅tan−1(−x2)+c\frac{1}{2} \cdot \tan ^{-1}\left(-x^{2}\right)+c21⋅tan−1(−x2)+c
Solve:=12∫2xdx1+(x2)2=12⋅tan−1(x2)+c =\frac{1}{2} \int \frac{2 x d x}{1+\left(x^{2}\right)^{2}}=\frac{1}{2} \cdot \tan ^{-1}\left(x^{2}\right)+c =21∫1+(x2)22xdx=21⋅tan−1(x2)+c
∫sin(5−x10)dx=f(x)+c \int \sin{\left ( 5 - \frac{x}{10} \right )} dx = f{\left ( x \right )} + c ∫sin(5−10x)dx=f(x)+c হলে, f(x)এর মান কত?
g(x)=x g(x)=\sqrt{x} g(x)=x হলে-
i. ∫1g(x)dx=2x+c \int \frac{1}{g(x)} d x=2 \sqrt{x}+c ∫g(x)1dx=2x+c
ii. ∫01g(x)dx=23 \int_{0}^{1} g(x) d x=\frac{2}{3} ∫01g(x)dx=32
iii. ∫sec2xdxg(tanx)=2tanx+c \int \frac{\sec ^{2} x d x}{g(\tan x)}=2 \sqrt{\tan x}+c ∫g(tanx)sec2xdx=2tanx+c
নিচের কোনটি সঠিক?
∫x9x4+4dx=? \int \frac{x}{9 x^{4} + 4} dx = ? ∫9x4+4xdx=?
∫cosx−1sinx+1;exdx\int { \cfrac { \cos { x } -1 }{ \sin { x } +1 } ; } { e }^{ x }dx∫sinx+1cosx−1;exdx is equal to:
