Solve ∫ 1^2dt/sqrt{e^2+1}

$$\int \frac { 1 ^ { 2 } d t } { \sqrt { e ^ { 2 } + 1 } }$$

Evaluate

$$\frac{t}{\sqrt{e^{2}+1}}+С$$

Solution Steps

Find the integral of \frac{1}{\sqrt{e^{2}+1}} using the table of common integrals rule \int a\mathrm{d}t=at.

$$\frac{1}{\sqrt{e^{2}+1}}t$$

Simplify.

$$\frac{t}{\sqrt{e^{2}+1}}$$

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

$$\frac{t}{\sqrt{e^{2}+1}}+С$$

Differentiate w.r.t. t

$$\frac{1}{\sqrt{e^{2}+1}}$$