frac{e^{x}3^{21ee^x/2}}{sece^x(3+3^(sine^x))}dx କୁ ସମାଧାନ କରନ୍ତୁ

$$\frac { e ^ { x } 3 ^ { \frac { 21 e e ^ { x } } { 2 } } } { \sec e ^ { x } ( 3 + 3 ^ { ( \sin e ^ { x } ) } ) } d x$$

ମୂଲ୍ୟାୟନ କରିବା

$$\frac{dxe^{x}\cos(e^{x})\times 3^{\frac{21e^{x+1}}{2}}}{3^{\sin(e^{x})}+3}$$

w.r.t. x ର ପ୍ରଭେଦ ଦର୍ଶାନ୍ତୁ

$$\frac{d\left(-2\ln(3)xe^{2x}\times 3^{\frac{21e^{x+1}+2\sin(e^{x})}{2}}\left(\cos(e^{x})\right)^{2}+21\ln(3)x\cos(e^{x})e^{2x+1}\times 3^{\frac{21e^{x+1}+2\sin(e^{x})}{2}}+2xe^{x}\cos(e^{x})\times 3^{\frac{21e^{x+1}+2\sin(e^{x})}{2}}-2xe^{2x}\sin(e^{x})\times 3^{\frac{21e^{x+1}+2\sin(e^{x})}{2}}+63\ln(3)x\cos(e^{x})e^{2x+1}\times 3^{\frac{21e^{x+1}}{2}}+6xe^{x}\cos(e^{x})\times 3^{\frac{21e^{x+1}}{2}}-6xe^{2x}\sin(e^{x})\times 3^{\frac{21e^{x+1}}{2}}+2e^{x}\cos(e^{x})\times 3^{\frac{21e^{x+1}+2\sin(e^{x})}{2}}+6e^{x}\cos(e^{x})\times 3^{\frac{21e^{x+1}}{2}}\right)}{2\left(3^{\sin(e^{x})}+3\right)^{2}}$$