Home/Calculus II/Trigonometric substitution and quadratic radicals/Fundamental formsSection 7.4Fundamental formsFormulavizCopy LaTeX∫dxa2−x2=arcsin (xa)+C,∣x∣<a\int\frac{dx}{\sqrt{a^2-x^2}} =\arcsin\!\left(\frac{x}{a}\right)+C, \qquad |x|<a∫a2−x2dx=arcsin(ax)+C,∣x∣<a∣x∣<a|x|<a∣x∣<aView detail →FormulaCopy LaTeX∫dxa2+x2=1aarctan (xa)+C,a>0\int\frac{dx}{a^2+x^2} =\frac{1}{a}\arctan\!\left(\frac{x}{a}\right)+C, \qquad a>0∫a2+x2dx=a1arctan(ax)+C,a>0a>0a>0a>0View detail →FormulaCopy LaTeX∫dxxx2−a2=1aarcsec ∣xa∣+C,∣x∣>a>0\int\frac{dx}{x\sqrt{x^2-a^2}} =\frac{1}{a}\operatorname{arcsec}\!\left|\frac{x}{a}\right|+C, \qquad |x|>a>0∫xx2−a2dx=a1arcsecax+C,∣x∣>a>0∣x∣>a>0|x|>a>0∣x∣>a>0View detail →FormulaCopy LaTeX∫dxx2+a2=ln∣x+x2+a2∣+C\int\frac{dx}{\sqrt{x^2+a^2}} =\ln\left|x+\sqrt{x^2+a^2}\right|+C∫x2+a2dx=lnx+x2+a2+CView detail →FormulaCopy LaTeX∫dxx2−a2=ln∣x+x2−a2∣+C\int\frac{dx}{\sqrt{x^2-a^2}} =\ln\left|x+\sqrt{x^2-a^2}\right|+C∫x2−a2dx=lnx+x2−a2+CView detail →
FormulavizCopy LaTeX∫dxa2−x2=arcsin (xa)+C,∣x∣<a\int\frac{dx}{\sqrt{a^2-x^2}} =\arcsin\!\left(\frac{x}{a}\right)+C, \qquad |x|<a∫a2−x2dx=arcsin(ax)+C,∣x∣<a∣x∣<a|x|<a∣x∣<aView detail →
FormulaCopy LaTeX∫dxa2+x2=1aarctan (xa)+C,a>0\int\frac{dx}{a^2+x^2} =\frac{1}{a}\arctan\!\left(\frac{x}{a}\right)+C, \qquad a>0∫a2+x2dx=a1arctan(ax)+C,a>0a>0a>0a>0View detail →
FormulaCopy LaTeX∫dxxx2−a2=1aarcsec ∣xa∣+C,∣x∣>a>0\int\frac{dx}{x\sqrt{x^2-a^2}} =\frac{1}{a}\operatorname{arcsec}\!\left|\frac{x}{a}\right|+C, \qquad |x|>a>0∫xx2−a2dx=a1arcsecax+C,∣x∣>a>0∣x∣>a>0|x|>a>0∣x∣>a>0View detail →
FormulaCopy LaTeX∫dxx2+a2=ln∣x+x2+a2∣+C\int\frac{dx}{\sqrt{x^2+a^2}} =\ln\left|x+\sqrt{x^2+a^2}\right|+C∫x2+a2dx=lnx+x2+a2+CView detail →
FormulaCopy LaTeX∫dxx2−a2=ln∣x+x2−a2∣+C\int\frac{dx}{\sqrt{x^2-a^2}} =\ln\left|x+\sqrt{x^2-a^2}\right|+C∫x2−a2dx=lnx+x2−a2+CView detail →