# Integral

Find $$\displaystyle \int \dfrac{dx}{4\sqrt2 \sin(3x) + 2\cos(3x)}$$ it is easy but my answer is in different form from answer given , what do you get in terms of tanx and logs ? and by using substitutions ?

Note by Brilliant Member
1 year, 7 months ago

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Write $4\sqrt{2}\sin3x + 2\cos3x \; = \; 6\cos(3x-\alpha) \hspace{2cm} \alpha = \cos^{-1}\tfrac13$ and the integral becomes $\int \tfrac16\sec(3x-\alpha)\,dx \; = \; \tfrac{1}{18}\ln\big|\sec(3x-\alpha)+\tan(3x-\alpha)\big| + c$

- 1 year, 7 months ago

Yes, I approached the same way.

- 1 year, 7 months ago

- 1 year, 7 months ago

1. Can you state the solution?
2. Did you remember the "+C" which means that $$\sin^2 + C = - \cos^2 +C$$?

Staff - 1 year, 7 months ago

What is the ANS?????

- 1 year, 7 months ago

Mark Hennings has given it.

- 1 year, 7 months ago