Integrate the following with respect to x : 2cos x - 4sin x + 5 sec² x + cosec² x

Evaluate the following integrals : \({12\over (4x-5)^3}+{6\over 3x+2}+16e^{4x+3}\)

Integrate the following with respect to x : \((x+4)^5+{5\over (2-5x)^4}-cosec^2(3x-1)\)

Integrate the following with respect to x : \(4cos(5-2x)+9e^{3x-6}+{24\over 6-4x}\)

Integrate the following with respect to x : \(sec^2{x\over 5}+18cos 2x+10sec(5x+3)tan(5x+3)\)

If f '(x) = 4x - 5 and f(2) = 1, find f(x).

If f'(x) = 9x² - 6x and f(0) = -3, find f(x).

Integrate the following with respect to x : \((1-x^3)^2\)

Integrate the following with respect to x : \({x^2-x+1\over x^3}\)

Evaluate : \(\int {1\over sin ^2x cos^2x}dx\)