Question

Calcule a seguinte integral:

Answer 1

$\displaystyle \int \text{sen}^4(\text x).\text{cos}^3(\text x)\text{dx} \\\\\\\ \int\text{sen}^4(\text x)\text{cos}^2(\text x)\text{cos(x)}\text{dx} \\\\\\ \int \text{sen}^4(\text x)[1-\text{sen}^2(\text x)]\text{cos(x)}\text{dx} \\\\ \underline{\text{fa{\c c}amos}}: \\\\\ \text u = \text{sen(x)}\to \text{du}=\text{cos(x)}\text{dx} \\\\\\ \int \text u^4[1-\text u^2]\text{du} \\\\\\ \int \text u^4.\text{du} - \int \text u^6.\text{du} \\\\\\ \frac{\text u^5}{5}-\frac{\text u^7}{7}+\text C$

$\huge\boxed{\displaystyle \frac{\text{sen}^5(\text x)}{5}-\frac{\text{sen}^7(\text x)}{7} +\text C \ }\checkmark$

letra C