Qn-e-2x-2-2x-6-dx-I-need-help-plz-

Question Number 73668 by liki last updated on 14/Nov/19

Q n . \int (e^{2 x^{2} + 2 x + 6}) d x

\dots I n e e d h e l p p l z . .

Answered by arkanmath7@gmail.com last updated on 14/Nov/19

= \int e^{2 x^{2} + 2 x} . e^{6} d x

= e^{6} \int e^{2 x^{2} + 2 x} d x

= e^{6} \int e^{2 x^{2} + 2 x + \frac{1}{2} - \frac{1}{2}} d x

= e^{6} \int e^{{(\sqrt{2} x + \frac{1}{\sqrt{2}})}^{2} - \frac{1}{2}} d x

= e^{- \frac{1}{2}} e^{6} \int e^{{(\frac{2 x + 1}{\sqrt{2}})}^{2}} d x

n o w l e t u = \frac{2 x + 1}{\sqrt{2}} \Rightarrow d u = \sqrt{2} d x

\Rightarrow d u = \sqrt{2} d x \Rightarrow d x = \frac{1}{\sqrt{2}} d u

\int e^{2 x^{2} + 2 x + 6} d x = e^{\frac{11}{2}} . \frac{1}{\sqrt{2}} \int e^{u^{2}} d u

= \frac{\sqrt{π} e^{\frac{11}{2}}}{2 \sqrt{2}} \int \frac{2 e^{u^{2}}}{\sqrt{π}} d u e r r o r f u n c t i o n

= \frac{\sqrt{π} e^{\frac{11}{2}}}{2 \sqrt{2}} e r f (u)

= \frac{\sqrt{π} e^{\frac{11}{2}}}{2 \sqrt{2}} e r f (\frac{2 x + 1}{\sqrt{2}}) + c

Commented by liki last updated on 14/Nov/19

T h a n k s s o m u c h . .

Commented by liki last updated on 14/Nov/19

well soln