integrate-with-respect-to-x-dx-9x-2-6x-10-

Question Number 21077 by j.masanja06@gmail.com last updated on 11/Sep/17

i n t e g r a t e w i t h r e s p e c t t o x

\int \frac{d x}{9 x^{2} + 6 x + 10}

Answered by Joel577 last updated on 12/Sep/17

9 x^{2} + 6 x + 1 + 9

I = \int \frac{d x}{{(3 x + 1)}^{2} + 9}

Let u = 3 x + 1 \to d u = 3 d x

I = \frac{1}{3} \int \frac{d u}{u^{2} + 9}

= \frac{1}{9} \tan^{- 1} (\frac{u}{3}) + C

= \frac{1}{9} \tan^{- 1} (x + \frac{1}{3}) + C

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