If _ 0 ^ x e^ 2 x e^ -z^ 2 d z=f(x) _ 0 ^ x e^ -z^ 2 / 4 d z then e^ x ( _ e (f(x))+ x 2…
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
If \(\int_{0}^{x} e^{2 x} \cdot e^{-z^{2}} d z=f(x) \int_{0}^{x} e^{-z^{2} / 4} d z\)
then \(\int e^{x}\left(\log _{e}(f(x))+\frac{x}{2}\right) d x=\)
then \(\int e^{x}\left(\log _{e}(f(x))+\frac{x}{2}\right) d x=\)
- \(\frac{x e^{x}}{2}+c\)
- \(\frac{x^{2} e^{x}}{4}+c\)
- \(\frac{x^{2} e^{x}}{2}+c\)
- \(\frac{x e^{x}}{4}+c\)
Answer
(B) x^ 2 e^ x 4 +c
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