Pembuktian tan x dx = -ln |cos x| + C


\int tan x dx = \int \frac{sin \quad x}{cos \quad x} dx

= \int \frac{sin \quad x}{cos \quad x} \quad \frac{d(cos \quad x)}{-sin \quad x}

= \int -\frac{1}{cos \quad x} d(cos x)

misal : cos x = u kemudian substitusi

= \int -\frac{1}{u} du

= -ln |u| + C

substitusi lagi u = cos x, sehingga

= -ln |cos x| + C \blacksquare

Iklan

2 comments on “Pembuktian tan x dx = -ln |cos x| + C

  1. Ping-balik: Pembuktian integral (tan x) dx | nysmiftahuljannah

Tinggalkan Balasan

Isikan data di bawah atau klik salah satu ikon untuk log in:

Logo WordPress.com

You are commenting using your WordPress.com account. Logout / Ubah )

Gambar Twitter

You are commenting using your Twitter account. Logout / Ubah )

Foto Facebook

You are commenting using your Facebook account. Logout / Ubah )

Foto Google+

You are commenting using your Google+ account. Logout / Ubah )

Connecting to %s