What is the integral of secx?
Find integration of secx.
Reframe the integral:
∫secxdx=∫secxsecx+tanxsecx+tanxdx∫secxdx=∫sec2x+secxtanxsecx+tanxdx...(1)
Take,secx+tanx=t⇒secxtanx+sec2xdx=dt.
To Find Put the above values in the equation (1):
∫secxdx=∫dtt∫secxdx=ln|t|+C∵∫dtt=ln|t|∫secxdx=ln|secx+tanx|+CPutt=secx+tanx
Hence, the required integral is ∫secxdx=ln|secx+tanx|+C where C is a constant of integration .
What is the geometrical interpretation of indefinite integral?
What is integral of (ax+b)/(cx+d)