Please help me solve this with a detailed solution Evaluate

Please help me solve this with a detailed solution. Evaluate based on either inverse trigonometric, hyperbolic functions or natural logarithms. (No Integral Tables)

Thanks!

Solution

Use substitution:

u = 2x

du = 2 dx

Therefore:

int dx/(1-4x²) =

int (1/2) du/(1-u²) =

(1/2) arcsin(u) + C =

(1/2) arcsin(2x) + C