61 problems.
- \(\int 2018^x\,dx\)
- \(\int\frac{\sin^3 x}{\cos x-\cos^3 x}\,dx\)
- \(\int\frac{\sin x}{\cos^2 x}\,dx\) and \(\int\csc(ax)\cot(ax)\,dx\)
- \(\int\frac{\cos x}{\sin^2 x}\,dx\)
- \(\int\frac{1}{9+x^2}\,dx\)
- \(\int_1^2\frac{dx}{x\sqrt{x^2-1}}\)
- \(\int_{\pi/3}^{\pi/2}\frac{1-\cos x}{\sin x}\,dx=\log\frac{3}{2}\)
- Antiderivatives of \((\sec^3 x+e^{\sin x})/\sec x\) and \(1/(\tan x+\cot x)\)
- \(\int\sin x\cos x\cot x\tan x\,dx\)
- \(\int\sqrt{1+\cos(2ax)}\,dx\)
- \(\int_{0}^{\pi} \sqrt{1 + \cos(2x)} \, dx\)
- \(\int_0^1\int_y^1\sin(x^2)\,dx\,dy\) by reversing the order of integration
- Gaussian integrals \(\int e^{-x^2}\,dx\) and \(\int e^{-(x-\mu)^2/(2\sigma^2)}\,dx\)
- Antiderivatives of \(\frac{xe^x\ln x-e^x}{x(\ln x)^2}\) and \((\tan x+\cot x)^2\)
- \(\int\sin(x)\cos(\cos(x))\,dx\)
- \(\int e^{\sin^2 x}\sin 2x\,dx\)
- Antiderivative of \(e^{x+e^x}\)
- Integrals of \(\frac{1}{x(\ln x)^2}\) and \(\frac{1}{x^2}\cos\frac{1}{x}\)
- The substitution \(u=1/x\)
- \(\int\frac{e^x}{e^x+1}\,dx\)
- Antiderivative of \(\frac{1+e^x}{1-e^x}\)
- Antiderivative of \(\frac{x+1}{x^2+2x+3}\)
- \(\int\frac{4x^3+2x}{x^4+1}\,dx\)
- \(\int\sqrt{4-x}\,dx\)
- Antiderivative of \(x\sqrt{x+1}\)
- \(\int\frac{x}{x^2+9}\,dx\)
- \(\int\frac{x}{1+x^4}\,dx\)
- \(\int\frac{x^2}{1+x^6}\,dx\)
- \(\int\frac{dx}{e^x+e^{-x}}\) and \(\int\frac{dx}{\sqrt{e^{2x}-1}}\)
- Integrals of \(\frac{\sqrt{1+\ln x}}{x\ln x}\), \(\frac{7-\ln x}{x(3+\ln x)}\), \(\frac{\sec^2 x}{1+\tan x}\), \(\frac{\sin x}{\sqrt{4-\cos^2 x}}\), and \(\frac{\sec^2 x}{\sqrt{9-\tan^2 x}}\)
- Antiderivatives by radical substitution, starting with \(\int\frac{1-\sqrt{x}}{1+\sqrt{x}}\,dx\)
- Integrals of \(1/\sqrt{x(1-x)}\), \(x/(1-x^2+\sqrt{1-x^2})\), and \(1/(x(x^2+1))\)
- Integrals of \(\sqrt{1-x^2}\), \(\sqrt{16-x^2}\) on \([-4,4]\), and \((1+x)\sqrt{1-x^2}\) on \([-1,1]\)
- Antiderivative of \(x^3/\sqrt{25-x^2}\)
- \(\int\frac{x+1}{\sqrt{4-x^2}}\,dx\)
- Antiderivative of \(\frac{x}{\sqrt{4-x^4}}\)
- \(\int\frac{\sqrt{x^2-a^2}}{x}\,dx\)
- Antiderivatives of \(1/(x^2\sqrt{x^2-a^2})\) and \(1/(x\sqrt{x^2-a^2})\)
- Antiderivatives of \(\frac{1}{\sqrt{x^2+25}}\) and \(\frac{1}{(1+x^2)^{3/2}}\)
- Integrals of \(\frac{x^2+2x+1}{x\sqrt{x^2-1}}\) and \(\frac{x+16}{\sqrt{x^2-4x+8}}\)
- \(\int\ln(ax+b)\,dx\) and logarithmic special cases
- Antiderivatives of \(x^n\ln x\)
- \(\int(\ln x)^2\,dx\) and the reduction formula for \(\int x^a e^{bx}\,dx\)
- Antiderivatives of \(e^{x^{1/a}}\), \(e^x\sin x\), and \(e^x\cos x\)
- \(\int e^x\cos x\,dx\) and \(\int\sin(\ln x)\,dx\)
- \(\int x\sec^{-1}(x)\,dx\) and \(\int x\csc^{-1}(x)\,dx\)
- Antiderivatives of \(x\arcsin(1/x)\), \(x\arctan x\), and \(x\sin(2x)\)
- Antiderivatives of \(\frac{x+\sin x}{1+\cos x}\) and \(\frac{xe^x}{(e^x+1)^2}\)
- Antiderivatives of \(\ln\sqrt{x^2+1}\) and \(\frac{2\arctan(e^x)}{e^{2x}}\)
- Partial-fraction antiderivatives of six rational functions
- Integrals of rational functions by long division and partial fractions
- Integrals of rational functions with \(x^2+1\) in the denominator
- Antiderivatives of powers of \(\sin x\) and \(\cos x\)
- Antiderivatives of trigonometric products of \(\sin x\) and \(\cos x\)
- Antiderivatives of powers of \(\sec x\) and \(\tan x\)
- Sum-to-product and product-to-sum identities for sine, cosine, and tangent
- Integrals of \(\cos(x+\pi/4)\cos(x-\pi/4)\), \(\sin(4x)\cos(3x)\), and \(\cos x\cos 2x\sin 3x\)
- Antiderivatives of \(\frac{1\pm\sin x}{1+\cos x}\) and \(\frac{1}{1+\sin x+\cos x}\)
- Antiderivatives of \(\frac{1}{\sin x+\cos x}\) and \(\frac{\sin x}{1\pm\sin x}\)
- Antiderivatives of \(\frac{x}{x^4-16}\) and \(\frac{x\tan^{-1}x}{(x^2+1)^2}\)
- Infinite nested-radical antiderivative and several trigonometric definite integrals