$$ \int \sqrt{1+x^{2}} d x $$ Risolvilo FACEOVDO $$ \quad x=\operatorname{tenh}(t) $$

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Calcolare l'integrale $$ \int \sqrt{1+x^{2}} d x $$.
Evaluate the integral by following steps:
- step0: Evaluate using formulas and rules:
  $$\int \sqrt{1+x^{2}} dx$$
- step1: Evaluate the integral:
  $$\frac{x}{2}\sqrt{1^{2}+x^{2}}+\frac{1^{2}}{2}\ln{\left(x+\sqrt{1^{2}+x^{2}}\right)}$$
- step2: Evaluate the power:
  $$\frac{x}{2}\sqrt{1^{2}+x^{2}}+\frac{1^{2}}{2}\ln{\left(x+\sqrt{1+x^{2}}\right)}$$
- step3: Evaluate the power:
  $$\frac{x}{2}\sqrt{1+x^{2}}+\frac{1^{2}}{2}\ln{\left(x+\sqrt{1+x^{2}}\right)}$$
- step4: Evaluate the power:
  $$\frac{x}{2}\sqrt{1+x^{2}}+\frac{1}{2}\ln{\left(x+\sqrt{1+x^{2}}\right)}$$
- step5: Multiply the terms:
  $$\frac{x\sqrt{1+x^{2}}}{2}+\frac{1}{2}\ln{\left(x+\sqrt{1+x^{2}}\right)}$$
- step6: Simplify the expression:
  $$\frac{1}{2}x\sqrt{1+x^{2}}+\frac{1}{2}\ln{\left(x+\sqrt{1+x^{2}}\right)}$$
- step7: Add the constant of integral C:
  $$\frac{1}{2}x\sqrt{1+x^{2}}+\frac{1}{2}\ln{\left(x+\sqrt{1+x^{2}}\right)} + C, C \in \mathbb{R}$$
La soluzione dell'integrale $$ \int \sqrt{1+x^{2}} d x $$ è $$ \frac{1}{2}x\sqrt{1+x^{2}} + \frac{1}{2}\ln{(x+\sqrt{1+x^{2}})} + C $$, dove $$ C $$ è una costante arbitraria.
L'integrale $$ \int \sqrt{1+x^{2}} d x $$ è uguale a $$ \frac{1}{2}x\sqrt{1+x^{2}} + \frac{1}{2}\ln{(x+\sqrt{1+x^{2}})} + C $$, dove $$ C $$ è una costante.

Risolvilo FACEOVDO

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