বিভিন্ন সূত্রের ব্যবহারে যোগজীকরণ
∫sinx1+cosxdx=?\int \frac{\sin x}{1+\cos x} d x = ?∫1+cosxsinxdx=?
−ln∣1+cosx∣+c-\ln |1+\cos x|+c−ln∣1+cosx∣+c
ln∣1+cosx∣+c\ln |1+\cos x|+cln∣1+cosx∣+c
−ln∣1−cosx∣+c-\ln |1-\cos x|+c−ln∣1−cosx∣+c
−ln∣1+sinx∣+c-\ln |1+\sin x|+c−ln∣1+sinx∣+c
Solve:
∫sinx1+cosxdx=−∫(−sinxdx)1+cosx=−ln∣1+cosx∣+c\begin{array}{l} \int \frac{\sin x}{1+\cos x} d x=-\int \frac{(-\sin x d x)}{1+\cos x} \\ \quad=-\ln |1+\cos x|+c \end{array} ∫1+cosxsinxdx=−∫1+cosx(−sinxdx)=−ln∣1+cosx∣+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:
