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$\int_{\Gamma}\left(\frac{e^{2}}{2\cdot(2^{2}+1)}\right)dz$

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Find indefinite integrals using the substitution

Full solution

Q.

\int_{\Gamma}\left(\frac{e^{2}}{2\cdot(2^{2}+1)}\right)dz

Pull Constants Out: We have the integral $\int \frac{e^{2}}{2(2^{2}+1)}dz$ . Since $e^2$ is a constant and $2^2 + 1$ is also a constant, we can pull them out of the integral. $\newline$ Calculation: $\int \frac{e^{2}}{2(2^{2}+1)}dz = \frac{e^{2}}{2(2^{2}+1)} \times \int 1dz$
Integrate $1$ : Now we integrate $1$ with respect to $z$ . $\newline$ Calculation: $\int(1)\,dz = z$
Substitute Integral of $1$ : Substitute the integral of $1$ back into the equation. $\newline$ Calculation: $\left(\frac{e^{2}}{2\cdot(2^{2}+1)}\right) \cdot z + C$
Simplify Constants: Simplify the constants. $\newline$ Calculation: (e^{\(2\)})/(\(2*( $4$ + $1$ )) * z + C = (e^{ $2$ })/( $2$ * $5$ ) * z + C = (e^{ $2$ })/( $10$ ) * z + C

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