evaluate the indefinite integral.\n int \frac{13}{16 + x^{2}} dx \ngive your answer in exact form. use ( c )…

evaluate the indefinite integral.\n int \frac{13}{16 + x^{2}} dx \ngive your answer in exact form. use ( c ) as the constant of integration.\n int \frac{13}{16 + x^{2}} dx =

evaluate the indefinite integral.\n int \frac{13}{16 + x^{2}} dx \ngive your answer in exact form. use ( c ) as the constant of integration.\n int \frac{13}{16 + x^{2}} dx =

Answer

Explicación:

Paso 1: Reconoce la forma de la integral

Recordamos la fórmula $\int\frac{1}{a^{2}+x^{2}}dx=\frac{1}{a}\arctan(\frac{x}{a})+C$. Aquí $a = 4$ y tenemos $\int\frac{13}{16 + x^{2}}dx=13\int\frac{1}{4^{2}+x^{2}}dx$.

Paso 2: Aplica la fórmula

Sustituyendo en la fórmula, obtenemos $13\times\frac{1}{4}\arctan(\frac{x}{4})+C$.

Respuesta:

$\frac{13}{4}\arctan(\frac{x}{4})+C$