বিভিন্ন সূত্রের ব্যবহারে যোগজীকরণ
∫x+25x−25dx=?\int \frac{x+25}{x-25} d x = ?∫x−25x+25dx=?
x+50ln∣x−25∣+cx+50 \ln |x-25|+cx+50ln∣x−25∣+c
x−50ln∣x−25∣+cx-50 \ln |x-25|+cx−50ln∣x−25∣+c
x+50ln∣x+25∣+cx+50 \ln |x+25|+cx+50ln∣x+25∣+c
−x+50ln∣x−25∣+c-x+50 \ln |x-25|+c−x+50ln∣x−25∣+c
Solve:
∫x+25x−25dx=∫x−25+50x−25dx=∫(x−25x−25+50x−25)dx=∫(1+50x−25)dx=∫dx+50∫1x−25dx=x+50ln∣x−25∣+c \begin{array}{l} \int \frac{x+25}{x-25} d x \\ =\int \frac{x-25+50}{x-25} d x=\int\left(\frac{x-25}{x-25}+\frac{50}{x-25}\right) d x \\ =\int\left(1+\frac{50}{x-25}\right) d x=\int d x+50 \int \frac{1}{x-25} d x \\ =x+50 \ln |x-25|+c \end{array} ∫x−25x+25dx=∫x−25x−25+50dx=∫(x−25x−25+x−2550)dx=∫(1+x−2550)dx=∫dx+50∫x−251dx=x+50ln∣x−25∣+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:
