Solve ∫ e^6dθ/1+e^6

$$\int \frac { e ^ { 6 } d \theta } { 1 + e ^ { 6 } }$$

Evaluate

$$\frac{e^{6}\theta }{e^{6}+1}+С$$

Solution Steps

Find the integral of \frac{e^{6}}{1+e^{6}} using the table of common integrals rule \int a\mathrm{d}\theta =a\theta .

$$\frac{e^{6}}{1+e^{6}}\theta$$

Simplify.

$$\frac{e^{6}\theta }{1+e^{6}}$$

If F\left(\theta \right) is an antiderivative of f\left(\theta \right), then the set of all antiderivatives of f\left(\theta \right) is given by F\left(\theta \right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\frac{e^{6}\theta }{1+e^{6}}+С$$

Differentiate w.r.t. θ

$$\frac{e^{6}}{e^{6}+1}$$