Evaluate the following improper integral eintinfin dxxlnx7

Question

Evaluate the following integral:

₁∫³₀∫^{x^2}(x² - 5 xy) dydx

Integrate ∫4x/(x²+1) dx

Integrate ∫e^3x-1 dx

Integrate ∫cos² (4x)dx

Integrate ∫2/x²+4dx

Integrate ∫7x-4/(x-1)² (x+2)dx

Integrate ∫x² sin(x) dx

Integrate ∫dx/(√(x² + 9)³

Evaluate the following improper integral: _e∫^∞ dx/x(ln(x))⁷

Evaluate the following improper integral: ₁∫ ^∞10/x⁶ dx

Evaluate the following improper integral: _-∞∫⁰ e^12x dx