find-the-indefinite-integralexe2x4ex13-dxintfracexe2x-4ex13dx

Question

Find the indefinite integral.∫exe2x−4ex+13 dx\int\frac{$$e^{x}$$}{$$e^{2x}$-4e^{x}+13$$}\,dx

Accepted Answer

13tan⁡−1(ex−23)+C\frac13\$$tan^{-1}$$\left(\frac{$$e^{x}-2$$}{3}\right)+C

Answer

3sin⁡−1(ex+23)+C3\$$sin^{-1}$$\left(\frac{$$e^{x}+2$$}{3}\right)+C

Answer

13sin⁡−1(ex−23)+C\frac13\$$sin^{-1}$$\left(\frac{$$e^{x}-2$$}{3}\right)+C

Answer

13tan⁡−1(ex+23)+C\frac13\$$tan^{-1}$$\left(\frac{$$e^{x}+2$$}{3}\right)+C

Find the indefinite integral.∫exe2x−4ex+13dx\(\int\]\frac{e^{x}\)}{e^{2x}-4e^{x}+13}\,dx