Final answer to the problem
$u=e^{-\frac{1}{2}k^2}$
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- Integrate by partial fractions
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1
Applying the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, in this case $n=1$
$\int\frac{-1}{u}du=\frac{1}{2}k^2$
Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation int(-1/u)du=int(k)dt. Applying the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, in this case n=1. Solve the integral \int\frac{-1}{u}du and replace the result in the differential equation. Multiply both sides of the equation by -1. Multiply the fraction and term in - \left(\frac{1}{2}\right)k^2.
Final answer to the problem
$u=e^{-\frac{1}{2}k^2}$
