Integral calculator

$$ \text{Find } \displaystyle\int \dfrac{\cos\left(4x\right)}{\sin\left(2x\right){\cdot}\cos\left(2x\right)}\, \mathrm d x $$

solution

$$ \displaystyle\int \dfrac{\cos\left(4x\right)}{\sin\left(2x\right){\cdot}\cos\left(2x\right)}\, \mathrm d x = {{\ln \left(\sin ^2\left(4\,x\right)+\cos ^2\left(4\,x\right)+2\, \cos \left(4\,x\right)+1\right)+\ln \left(\sin ^2\left(2\,x\right)+ \cos ^2\left(2\,x\right)+2\,\cos \left(2\,x\right)+1\right)+\ln \left(\sin ^2x+\cos ^2x+2\,\cos x+1\right)+\ln \left(\sin ^2x+\cos ^2x-2\,\cos x+1\right)}\over{4}} $$

1. For powers use ^. Example: $ x^{12} = $ x^12 ; $e^{x+2} = $ e^(x+2)

2. For square root use "sqrt". Example: $ \sqrt{x+1} = $ sqrt(x+1).

3. Supported constants: e, pi

4. Supported functions: sqrt, ln ( use 'ln' instead of 'log'), e (use 'e' instead of 'exp')

Trigonometric functions: sin cos tan cot sec csc

Inverse trigonometric functions: acos asin atan acot asec acsc

Hyperbolic functions: sinh, cosh, tanh, coth, sech, csch