Question

solve the integration ​

Answer 1

Answer:

Step-by-step explanation:

hope it helps you

Answer 2

$\sf\large\red{\underline{\underline{Question}}}:$

• $\displaystyle \sf Evaluate\; : \int\bf x\; e^{2x} \;dx$

$\sf\large\red{\underline{\underline{Solution}}}:$

$=\displaystyle \sf \int x\; e^{2x} \;dx$

$=\displaystyle x.\dfrac{e^{2x}}{2}-\int 1.\dfrac{e^{2x}}{2} \;dx$ {Integrating by parts}

$=\displaystyle x.\dfrac{e^{2x}}{2}-\dfrac{1}{2}\int \dfrac{e^{2x}}{2} \;dx$

$=\displaystyle x.\dfrac{e^{2x}}{2}-\dfrac{1}{2}.\dfrac{e^{2x}}{2}+\sf c$

$=\displaystyle \dfrac{xe^{2x}}{2}-\dfrac{e^{2x}}{4}+\sf c$

Therefore,

$\displaystyle \sf \int x\; e^{2x} \;dx =\displaystyle \dfrac{xe^{2x}}{2}-\dfrac{e^{2x}}{4}+\sf c$