Integrals

(the database of solved problems)

All the problems and solutions shown below were generated using the Integral Calculator.

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ID	Problem	Count
1951	$$ \displaystyle\int \sin\left(a+x\right)\, \mathrm d x $$	2
1952	$$ \displaystyle\int \ln\left(x\right)\, \mathrm d x $$	2
1953	$$ \int {1}\cdot{000143}{\exp{{\left({\cos{{\left({80}\right)}}}\right)}}} \, d\,x $$	2
1954	$$ \displaystyle\int^{3}_{0} \sqrt{x}+{x}^{\frac{1}{5}}+{x}^{\frac{1}{9}}\, \mathrm d x $$	2
1955	$$ \displaystyle\int^{8}_{4} {\mathrm{e}}^{x}\, \mathrm d x $$	2
1956	$$ $$	2
1957	$$ \displaystyle\int^{1}_{0} \dfrac{1}{\sqrt{3x+1}}\, \mathrm d x $$	2
1958	$$ $$	2
1959	$$ $$	2
1960	$$ \displaystyle\int \dfrac{\sqrt{x}+1}{x}\, \mathrm d x $$	2
1961	$$ $$	2
1962	$$ $$	2
1963	$$ $$	2
1964	$$ \displaystyle\int \cos\left(x\right){\cdot}{\mathrm{e}}^{-i{\cdot}ax}\, \mathrm d x $$	2
1965	$$ $$	2
1966	$$ $$	2
1967	$$ $$	2
1968	$$ \displaystyle\int \ln\left(x+1\right){\cdot}\cos\left(\dfrac{x}{2}\right)\, \mathrm d x $$	2
1969	$$ \displaystyle\int \ln\left(x+1\right){\cdot}\cos\left(\dfrac{3x}{2}\right)\, \mathrm d x $$	2
1970	$$ \displaystyle\int \ln\left(x+1\right){\cdot}\sin\left(\dfrac{x}{2}\right)\, \mathrm d x $$	2
1971	$$ \displaystyle\int \ln\left(x+1\right){\cdot}\sin\left(\dfrac{3x}{2}\right)\, \mathrm d x $$	2
1972	$$ \displaystyle\int \dfrac{1}{rx+{x}^{3}}\, \mathrm d x $$	2
1973	$$ $$	2
1974	$$ $$	2
1975	$$ $$	2
1976	$$ $$	2
1977	$$ $$	2
1978	$$ $$	2
1979	$$ $$	2
1980	$$ $$	2
1981	$$ \displaystyle\int \dfrac{1}{x{\cdot}\left(5000-x\right)}\, \mathrm d x $$	2
1982	$$ \displaystyle\int \dfrac{x}{x+1}\, \mathrm d x $$	2
1983	$$ $$	2
1984	$$ $$	2
1985	$$ $$	2
1986	$$ $$	2
1987	$$ \displaystyle\int^{4}_{1} 2{x}^{2}-2x\, \mathrm d x $$	2
1988	$$ \displaystyle\int^{6}_{4+2^0.5} \sqrt{\dfrac{4{x}^{2}}{{\left(x-4\right)}^{2}}-{x}^{2}}\, \mathrm d x $$	2
1989	$$ \displaystyle\int^{6}_{4+2^1/2} sqsq{\cdot}\sqrt{t}{\cdot}t{\cdot}\left(\dfrac{4{x}^{2}}{{\left(x-4\right)}^{2}}-{x}^{2}\right)\, \mathrm d x $$	2
1990	$$ \displaystyle\int^{6}_{4+1.41} sqsqsq{\cdot}\sqrt{t}{\cdot}tt{\cdot}\left(\dfrac{4{x}^{2}}{{\left(x-4\right)}^{2}}-{x}^{2}\right)\, \mathrm d x $$	2
1991	$$ \displaystyle\int^{6}_{5.41} \sqrt{\dfrac{4{x}^{2}}{{\left(x-4\right)}^{2}}-{x}^{2}}\, \mathrm d x $$	2
1992	$$ \displaystyle\int^{6}_{4+1.41} \sqrt{\dfrac{4{x}^{2}}{{\left(x-4\right)}^{2}}-{x}^{2}}\, \mathrm d x $$	2
1993	$$ $$	2
1994	$$ $$	2
1995	$$ \displaystyle\int {x}^{4}{\cdot}{\left(2+\dfrac{3}{x}\right)}^{4}\, \mathrm d x $$	2
1996	$$ \displaystyle\int \dfrac{x-3}{3{x}^{2}+2x-5}\, \mathrm d x $$	2
1997	$$ $$	2
1998	$$ $$	2
1999	$$ \displaystyle\int \dfrac{1}{{\left(1+x\right)}^{\frac{1}{2}}}\, \mathrm d x $$	2
2000	$$ \displaystyle\int \dfrac{1}{{\left(1-x\right)}^{\frac{1}{2}}}\, \mathrm d x $$	2