Question

Calcule a integral indefinida

r) $\int\ {}(2e^2- \frac{senx}{cosx} +\frac{2}{x^7}) \, dx$

Answer 1

Oi Lucas

∫ (2e² - sen(x)/cos(x) + 2/x⁷) dx =

∫ 2e² dx - ∫ tg(x) dx + 2 ∫ 1/x⁷ dx = 2e²x + ln(cos(x)) - 1/(3x⁶) + C 

Answer 2

$\sf \displaystyle \int \left(2e^2-\frac{sen\:x}{cos\:x}+\frac{2}{x^7}\right)dx\\\\\\=\int \:2e^2dx-\int \frac{\sin \left(x\right)}{\cos \left(x\right)}dx+\int \frac{2}{x^7}dx\\\\\\=2e^2x-\left(-\ln \left|\cos \left(x\right)\right|\right)-\frac{1}{3x^6}\\\\\\=2e^2x+\ln \left|\cos \left(x\right)\right|-\frac{1}{3x^6}\\\\\\\to \boxed{\sf =2e^2x+\ln \left|\cos \left(x\right)\right|-\frac{1}{3x^6}+C}$