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
1001	$$ \displaystyle\int \dfrac{{x}^{2}}{{x}^{4}+1}\, \mathrm d x $$	2
1002	$$ \displaystyle\int^{6}_{0} 3{x}^{2}-6x-3\, \mathrm d x $$	2
1003	$$ \displaystyle\int^{6}_{0} 3{x}^{2}+6x-3\, \mathrm d x $$	2
1004	$$ \displaystyle\int^{6}_{0} 3{x}^{2}+6x+3\, \mathrm d x $$	2
1005	$$ \displaystyle\int {x}^{2}{\cdot}\ln\left(1+x\right)\, \mathrm d x $$	2
1006	$$ \displaystyle\int^{10}_{0} 3{x}^{2}-2x+1\, \mathrm d x $$	2
1007	$$ \displaystyle\int^{5}_{0} -{x}^{3}+3{x}^{2}-2x+6\, \mathrm d x $$	2
1008	$$ $$	2
1009	$$ \displaystyle\int \dfrac{8{\cdot}\left(x-1\right)}{\sqrt{{\left(2x-1\right)}^{3}}}\, \mathrm d x $$	2
1010	$$ \displaystyle\int \sqrt{2}{\cdot}x\, \mathrm d x $$	2
1011	$$ \displaystyle\int sq{\cdot}\sqrt{t}{\cdot}\left({x}^{2}-ax\right)\, \mathrm d x $$	2
1012	$$ \displaystyle\int \dfrac{1}{{\left(3{x}^{2}+1\right)}^{\frac{3}{2}}}\, \mathrm d x $$	2
1013	$$ \displaystyle\int {\left(50+25{\cdot}\cos\left(x\right)\right)}^{0.5}\, \mathrm d x $$	2
1014	$$ \displaystyle\int^{2\pi}_{0} {\left(50+25{\cdot}\cos\left(x\right)\right)}^{0.5}\, \mathrm d x $$	2
1015	$$ \displaystyle\int^{\pi}_{\pi/2} {\pi}-x\, \mathrm d x $$	2
1016	$$ \displaystyle\int^{\pi}_{--\pi} \cos\left(x\right)\, \mathrm d x $$	2
1017	$$ \displaystyle\int^{2}_{----1} {x}^{4}\, \mathrm d x $$	2
1018	$$ \displaystyle\int^{2}_{1.414} \dfrac{x}{{x}^{2}-1}\, \mathrm d x $$	2
1019	$$ \displaystyle\int^{0}_{\pi/6} \dfrac{\cos\left(x\right)}{1+2{\cdot}\sin\left(x\right)}\, \mathrm d x $$	2
1020	$$ \displaystyle\int^{\pi/6}_{0} \dfrac{\cos\left(x\right)}{1+2{\cdot}\sin\left(x\right)}\, \mathrm d x $$	2
1021	$$ \displaystyle\int^{1/6}_{0} \dfrac{1}{\sqrt{1-9{x}^{2}}}\, \mathrm d x $$	2
1022	$$ \displaystyle\int^{e}_{1} x{\cdot}\ln\left(x\right)\, \mathrm d x $$	2
1023	$$ \displaystyle\int^{\pi/2}_{0} x{\cdot}\sin\left(x\right)\, \mathrm d x $$	2
1024	$$ \displaystyle\int {\left(2{\cdot}\sin\left(x\right)-\sin\left(2\right){\cdot}x\right)}^{2}\, \mathrm d x $$	2
1025	$$ \displaystyle\int^{9}_{0} {\left(\sec\left(x\right)\right)}^{3}\, \mathrm d x $$	2
1026	$$ \displaystyle\int 5{\cdot}\cos\left(60{\pi}{\cdot}t\right)\, \mathrm d x $$	2
1027	$$ \displaystyle\int -4{\cdot}\left({x}^{3}+1\right){\cdot}{\left(x-3\right)}^{2}\, \mathrm d x $$	2
1028	$$ \displaystyle\int^{\infty}_{3} \dfrac{1}{x{\cdot}{\left(\ln\left(x\right)\right)}^{2}}\, \mathrm d x $$	2
1029	$$ \displaystyle\int^{\infty}_{1} \dfrac{x}{{\left(1+{x}^{2}\right)}^{2}}\, \mathrm d x $$	2
1030	$$ \displaystyle\int^{\infty}_{1} x{\cdot}{\mathrm{e}}^{-{x}^{2}}\, \mathrm d x $$	2
1031	$$ \displaystyle\int 20{\cdot}\cos\left(10t+\dfrac{{\pi}}{6}\right)\, \mathrm d x $$	2
1032	$$ \displaystyle\int^{10}_{3} x\, \mathrm d x $$	2
1033	$$ \displaystyle\int^{\pi/2}_{0} {\left(\cos\left(\dfrac{x}{2}\right)\right)}^{2}\, \mathrm d x $$	2
1034	$$ \displaystyle\int^{\pi}_{0} {\mathrm{e}}^{\cos\left(x\right)}{\cdot}\sin\left(2x\right)\, \mathrm d x $$	2
1035	$$ $$	2
1036	$$ \displaystyle\int \sqrt{1+{x}^{2}}{\cdot}\sqrt{\sqrt{1+{x}^{4}}}\, \mathrm d x $$	2
1037	$$ $$	2
1038	$$ $$	2
1039	$$ $$	2
1040	$$ $$	2
1041	$$ \displaystyle\int^{e}_{1} \ln\left(7x\right)\, \mathrm d x $$	2
1042	$$ $$	2
1043	$$ \displaystyle\int^{9}_{3} \sqrt{1+x{\cdot}{\left({x}^{2}+2\right)}^{\frac{1}{2}}}\, \mathrm d x $$	2
1044	$$ \displaystyle\int 6400{x}^{2}\, \mathrm d x $$	2
1045	$$ $$	2
1046	$$ \displaystyle\int \mathrm{e}+1\, \mathrm d x $$	2
1047	$$ \displaystyle\int {x}^{\frac{3}{2}}\, \mathrm d x $$	2
1048	$$ \displaystyle\int \dfrac{1}{2}{\cdot}x\, \mathrm d x $$	2
1049	$$ \displaystyle\int \dfrac{2}{9}\, \mathrm d x $$	2
1050	$$ \displaystyle\int \dfrac{2x}{9}\, \mathrm d x $$	2