If \( \int_{0}^{x} e^{z x} \cdot e^{-z^{2}} d z=f(x) \int_{0}^{x} e^{-z^{2} / 4} d z \) then \( ....

Channel:
PW Solutions
Subscribers:
443,000
Published on ● Video Link: https://www.youtube.com/watch?v=CM9P7C2vtQs


Duration: 6:11
0 views
0

If \( \int_{0}^{x} e^{z x} \cdot e^{-z^{2}} d z=f(x) \int_{0}^{x} e^{-z^{2} / 4} d z \)
\( \mathrm{P} \)
then \( \int e^{x}\left(\log _{e}(f(x))+\frac{x}{2}\right) d x= \)
(1) \( \frac{x e^{x}}{2}+c \)
(2) \( \frac{x^{2} e^{x}}{4}+c \)
(3) \( \frac{x^{2} e^{x}}{2}+c \)
(4) \( \frac{x e^{x}}{4}+c \)
.


📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


2024-01-22The domain of \( f(x)=\ln |\ln x| \) is....
2024-01-22If the initial pressure of a gas \( 0.03 \mathrm{~atm} \), the mass of the gas absorbed per gram....
2024-01-22Which of the following statements are true? (1) \( \int_{-\pi / 2}^{\pi / 2} \frac{\pi^{\sin x}}....
2024-01-22\( I_{n}=\int_{0}^{\pi / 2} \frac{\sin (2 n+1) x}{\sin x} d x \), then....
2024-01-22\( J_{n}=\int_{0}^{\pi / 2}\left(\frac{\sin n x}{\sin x}\right)^{2} d x \) and \( I_{n}=\int_{0}....
2024-01-22Match the items of Column I to those of Column II. \begin{tabular}{|l|l|l|l|} \hline & Column I ....
2024-01-22If \( a \neq b \) and \( a f(x)+b f\left(\frac{1}{x}\right)=\frac{1}{x}-5 \) for all \( x \neq 0....
2024-01-22\( I_{n}=\int_{-\pi}^{\pi} \frac{\sin n x}{\left(1+\pi^{x}\right) \sin x} d x, \quad n=0,1,2, \l....
2024-01-22\( f(x)=\int_{0}^{x} \cos ^{4} t d t \), then \( f(x+\pi) \) equals....
2024-01-22If \( I_{1}=\int_{-4}^{-5} e^{(x+5)^{2}} d x \) and \( I_{2}=3 \int_{1 / 3}^{2 / 3} e^{9[x-(2 / ....
2024-01-22If \( \int_{0}^{x} e^{z x} \cdot e^{-z^{2}} d z=f(x) \int_{0}^{x} e^{-z^{2} / 4} d z \) then \( ....
2024-01-22\( \int_{0}^{\log _{e} 5} \frac{e^{x} \sqrt{e^{x}-1}}{e^{x}+3} d x= \) (1) \( 3+\pi \) (2) \( 3-....
2024-01-22Solution of the equation \( \int_{\log _{e} 2}^{x} \frac{d t}{\sqrt{e^{t}-1}}=\frac{\pi}{6} \) i....
2024-01-22\( \int_{-\pi / 3}^{-\pi / 6} \frac{d x}{1+\tan ^{4} x}= \)....
2024-01-22Match the Column-I with Column-II \begin{tabular}{|l|l|l|l|} \hline \multicolumn{2}{|c|}{ Column....
2024-01-22\( \int_{0}^{\pi} \frac{x \sin x}{1+\cos ^{2} x} d x= \)....
2024-01-22Match the statements/expressions in Column-I with the values given in Column II: \begin{tabular}....
2024-01-22\( \int_{0}^{\pi} x f(\sin x) d x=k \int_{0}^{\pi / 2} f(\sin x) d x \), the value of \( k \) is....
2024-01-22\( \int_{0}^{10} e^{x-[x]} d x([\cdot] \) denotes integral part \( ) \) is equal to....
2024-01-22If a vector \( \vec{r} \) satisfies the equation \( \vec{r} \times(\hat{i}+2 \hat{j}+\hat{k})=\h....
2024-01-22What is the distance between the planes \( x-2 y+z-1=0 \) and \( -3 x+6 y-3 z+2=0 \) ?....