Question

Encontre a integral das funções:
1) ∫ 6x⁴ dx
2)∫ (5x⁻⁴₋ 8x⁻³) dx

Answer 1

Resposta e Explicação passo a passo:

Questão 1

$\int \:6x^4dx\\\\=6\cdot \int \:x^4dx\\\\=6\cdot \frac{x^{4+1}}{4+1}\\\\=\frac{6x^5}{5}\\\\=\frac{6x^5}{5}+C$

Questão 2

$\int \left(5x^{-4}-\:8x^{-3}\right)\:dx\\\\\mathrm{Aplicar\:a\:regra\:da\:soma}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\\\=\int \:5x^{-4}dx-\int \:8x^{-3}dx\\\\=-\frac{5}{3x^3}-\left(-\frac{4}{x^2}\right)\\\\=-\frac{5}{3x^3}+\frac{4}{x^2}\\\\=-\frac{5}{3x^3}+\frac{4}{x^2}+C$