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
1451	$$ $$	2
1452	$$ $$	2
1453	$$ $$	2
1454	$$ $$	2
1455	$$ $$	2
1456	$$ \displaystyle\int^{2\pi}_{0} \sqrt{{\left(\dfrac{3}{2}\right)}^{2}-{\left(x-\dfrac{5}{2}\right)}^{2}}\, \mathrm d x $$	2
1457	$$ \displaystyle\int^{4}_{0} \sqrt{1+{\left(\dfrac{-\left(x-\dfrac{5}{2}\right)}{{\left({\left(\dfrac{3}{2}\right)}^{2}-{\left(x-\dfrac{5}{2}\right)}^{2}\right)}^{\frac{1}{2}}}\right)}^{2}}\, \mathrm d x $$	2
1458	$$ \displaystyle\int \sin\left(3x\right){\cdot}\cos\left(4x\right)\, \mathrm d x $$	2
1459	$$ \int^{\pi/2}_{-\pi/2} \frac{{1}}{{\cos{{\left(\frac{{x}}{{2}}\right)}}}} \, d\,x $$	2
1460	$$ $$	2
1461	$$ $$	2
1462	$$ $$	2
1463	$$ $$	2
1464	$$ $$	2
1465	$$ $$	2
1466	$$ $$	2
1467	$$ \int^{2}_{1} {x}{\cos{{\left({x}\right)}}} \, d\,x $$	2
1468	$$ \displaystyle\int \dfrac{\ln\left(2x+1\right)}{x{\cdot}\left(x+1\right)}\, \mathrm d x $$	2
1469	$$ $$	2
1470	$$ \displaystyle\int^{\infty }_{0} {\mathrm{e}}^{{x}^{2}}{\cdot}\sin\left(x\right)\, \mathrm d x $$	2
1471	$$ \displaystyle\int^{\infty }_{0} \dfrac{\sin\left(x\right){\cdot}\cos\left(x\right)}{x}\, \mathrm d x $$	2
1472	$$ \displaystyle\int^{\infty }_{0} {\mathrm{e}}^{-{x}^{2}}\, \mathrm d x $$	2
1473	$$ \displaystyle\int^{1}_{0} {\mathrm{e}}^{-{x}^{2}}\, \mathrm d x $$	2
1474	$$ \displaystyle\int^{1}_{-\infty} \dfrac{{\mathrm{e}}^{-{x}^{2}}}{{\left(2{\pi}\right)}^{0.5}}\, \mathrm d x $$	2
1475	$$ \displaystyle\int \dfrac{1}{\left(1+{x}^{3}\right){\cdot}\left(1+{x}^{2}\right)}\, \mathrm d x $$	2
1476	$$ \displaystyle\int^{2}_{1} {x}^{3}{\cdot}\sqrt{{x}^{4}+1}\, \mathrm d x $$	2
1477	$$ \displaystyle\int 3{x}^{2}-2x+2\, \mathrm d x $$	2
1478	$$ \displaystyle\int^{-1}_{-1} 3{x}^{2}-2x+2\, \mathrm d x $$	2
1479	$$ \displaystyle\int {\left({x}^{2}+\sqrt{x}\right)}^{2}\, \mathrm d x $$	2
1480	$$ \displaystyle\int {4}^{3}x\, \mathrm d x $$	2
1481	$$ \displaystyle\int {4}^{3x}\, \mathrm d x $$	2
1482	$$ \displaystyle\int^{\pi/2}_{0} {\left(\sin\left(2\right){\cdot}x\right)}^{12}{\cdot}\cos\left(2\right){\cdot}x\, \mathrm d x $$	2
1483	$$ \displaystyle\int^{0}_{1} {x}^{2}\, \mathrm d x $$	2
1484	$$ \displaystyle\int^{1}_{0} -{x}^{2}+1\, \mathrm d x $$	2
1485	$$ \displaystyle\int^{2}_{0} 2x-{x}^{2}\, \mathrm d x $$	2
1486	$$ \displaystyle\int^{1}_{-1} -{x}^{2}+3-2\, \mathrm d x $$	2
1487	$$ \displaystyle\int^{1}_{-1} {x}^{\frac{1}{2}}+4-4\, \mathrm d x $$	2
1488	$$ \displaystyle\int^{2}_{-2} -{x}^{2}+6-2\, \mathrm d x $$	2
1489	$$ \displaystyle\int^{-\pi/2}_{\pi/2} 2{\cdot}\csc\left(x\right)-\csc\left(x\right)\, \mathrm d x $$	2
1490	$$ \displaystyle\int {\mathrm{e}}^{-{x}^{2}}\, \mathrm d x $$	2
1491	$$ \displaystyle\int {\mathrm{e}}^{\frac{-{x}^{2}}{2}}\, \mathrm d x $$	2
1492	$$ \displaystyle\int^{\pi}_{\pi/2} \sin\left(x\right)-\cos\left(x\right)\, \mathrm d x $$	2
1493	$$ $$	2
1494	$$ $$	2
1495	$$ \displaystyle\int \sqrt{x}{\cdot}\ln\left(2x\right)\, \mathrm d x $$	2
1496	$$ \displaystyle\int \dfrac{\cos\left(3\right){\cdot}\sqrt{x}}{\sqrt{x}}\, \mathrm d x $$	2
1497	$$ \displaystyle\int \dfrac{1}{\left({x}^{4}+1\right){\cdot}{x}^{2}}\, \mathrm d x $$	2
1498	$$ \displaystyle\int^{\infty}_{0} \dfrac{\sqrt{x}}{\left(x+1\right){\cdot}\left(x+2\right){\cdot}\left(x+3\right)}\, \mathrm d x $$	2
1499	$$ \displaystyle\int {x}^{n}{\cdot}{\left(\cosh\left(x\right)\right)}^{n}{\cdot}ax\, \mathrm d x $$	2
1500	$$ \displaystyle\int^{1}_{0} \dfrac{32}{x+4}\, \mathrm d x $$	2