Trig formulas

• d/dx(cos^-1 x) = -1/√(1-x^2)
• d/dx(sin^-1 x) = 1/√(1-x^2)
• $\int_{ }^{ }\ln\left(\sqrt{x}\right)dx$

  = $\int_{ }^{ }\ln\left(x^{\frac{1}{2}}\right)dx$

  = $\int_{ }^{ }\frac{1}{2}\ln\left(x\right)dx$
• $\int_{ }^{ }\sin\left(2x\right)dx$

  = $-\frac{1}{2}\cos\left(2x\right) +$$C$
• $\int_{ }^{ }\frac{1}{\sqrt{1-x^{2}}}dx$

  = sin^-1(x)
• $\int_{ }-^{ }\frac{1}{\sqrt{1-x^{2}}}dx$

  = cos^-1(x)
• $\int_{ }^{ }\frac{1}{1+x^{2}}dx$

  = tan^-1(x)
• 1/cos(x) = sec(x)
• 1/sin(x) = csc(x)
• 1/tan(x) = cot(x)
• int ( 1/ (a^2 + x^2 )) dx

  = $\frac{1}{a}\tan^{-1}\left(\frac{u}{a}\right)+$$C$
• cos(2x) = cos^2(x) - sin^2(x)