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
901	$$ \displaystyle\int^{2}_{1} {x}^{\frac{1}{3}}\, \mathrm d x $$	2
902	$$ \displaystyle\int^{7}_{1} \dfrac{1}{\sqrt{2x+2}}\, \mathrm d x $$	2
903	$$ \displaystyle\int^{4}_{1} \dfrac{{x}^{4}-8}{{x}^{2}}\, \mathrm d x $$	2
904	$$ \displaystyle\int^{\pi/2}_{0} 4x+3+\cos\left(x\right)\, \mathrm d x $$	2
905	$$ \displaystyle\int^{3}_{-1} \dfrac{1}{{\left(x+2\right)}^{2}}\, \mathrm d x $$	2
906	$$ \displaystyle\int^{-2}_{-4} {x}^{2}+\dfrac{1}{{x}^{3}}\, \mathrm d x $$	2
907	$$ \displaystyle\int^{3}_{1} \dfrac{{x}^{2}+1}{\sqrt{{x}^{3}+3x}}\, \mathrm d x $$	2
908	$$ \displaystyle\int^{4}_{0} \sqrt{x}-(\sqrt{2x+1})\, \mathrm d x $$	2
909	$$ \displaystyle\int^{-1}_{-4} \dfrac{1-{x}^{4}}{{x}^{2}}\, \mathrm d x $$	2
910	$$ \displaystyle\int 2{\mathrm{e}}^{x}+\dfrac{3}{x}+\dfrac{2}{{x}^{2}}\, \mathrm d x $$	2
911	$$ $$	2
912	$$ \displaystyle\int {x}^{4}{\cdot}{\left({\left(\tanh\left(x\right)\right)}^{5}\right)}^{3}{\cdot}{\left({\left(\mathrm{sech}\left(x\right)\right)}^{5}\right)}^{2}\, \mathrm d x $$	2
913	$$ \displaystyle\int {\mathrm{e}}^{-{x}^{2}}\, \mathrm d x $$	2
914	$$ \displaystyle\int^{-2}_{-4} \dfrac{2}{{x}^{3}}\, \mathrm d x $$	2
915	$$ \displaystyle\int \dfrac{1}{{x}^{3}}\, \mathrm d x $$	2
916	$$ \displaystyle\int^{\pi/2}_{0} \sqsqrtt{1}+4{\cdot}{\left(\cos\left(2x\sqrtight)\sqrtight)}^{2}\, \mathsqrtm d x $$	2
917	$$ \displaystyle\int^{\pi/2}_{0} \sqrt{1+4{\cdot}{\left(\cos\left(2x\right)\right)}^{2}}\, \mathrm d x $$	2
918	$$ \displaystyle\int^{5}_{-5} {x}^{2}-2\, \mathrm d x $$	2
919	$$ \displaystyle\int^{\pi/2}_{0} \dfrac{\sin\left(x\right){\cdot}\cos\left(x\right)}{{\left(\cos\left(x\right)\right)}^{4}+{\left(\sin\left(x\right)\right)}^{4}}\, \mathrm d x $$	2
920	$$ \displaystyle\int {\mathrm{e}}^{-\left(2+\frac{1}{x}\right)}\, \mathrm d x $$	2
921	$$ \displaystyle\int c{\cdot}\left(1-{x}^{2}\right)\, \mathrm d x $$	2
922	$$ \displaystyle\int 1-{x}^{2}\, \mathrm d x $$	2
923	$$ \displaystyle\int \dfrac{{x}^{3}}{\sqrt{{x}^{2}+100}}\, \mathrm d x $$	2
924	$$ \displaystyle\int^{4}_{1} 3{t}^{3}+4{\mathrm{e}}^{3t}+\dfrac{2}{3}+4{\cdot}\cos\left(3t\right)\, \mathrm d x $$	2
925	$$ \displaystyle\int 10x{\cdot}{\left({x}^{2}+3\right)}^{4}\, \mathrm d x $$	2
926	$$ \displaystyle\int^{1}_{0} {x}^{2}{\cdot}{\mathrm{e}}^{3x}{\cdot}\left(1+x\right)\, \mathrm d x $$	2
927	$$ \displaystyle\int^{5}_{1} x{\cdot}\sqrt{5}{\cdot}{x}^{2}-4\, \mathrm d x $$	2
928	$$ \displaystyle\int \dfrac{{x}^{2}-14x}{{\left(x-7\right)}^{2}}\, \mathrm d x $$	2
929	$$ \displaystyle\int \dfrac{1}{{x}^{2}{\cdot}\sqrt{16-{x}^{2}}}\, \mathrm d x $$	2
930	$$ \displaystyle\int^{10}_{0} 5-6x+{x}^{2}\, \mathrm d x $$	2
931	$$ \int^{\pi}_{0} {2}\sqrt{{{2}-{\cos{{\left({x}\right)}}}}}^{{2}}+\sqrt{{{2}{\sin{{\left({x}\right)}}}}}^{{2}} \, d\,x $$	2
932	$$ \displaystyle\int \dfrac{1}{4}{\cdot}\tan\left(x\right)\, \mathrm d x $$	2
933	$$ \displaystyle\int \dfrac{1}{4{\cdot}\tan\left(x\right)}\, \mathrm d x $$	2
934	$$ \displaystyle\int^{\pi}_{0} \dfrac{x{\cdot}\sin\left(x\right)}{3+\cos\left(2x\right)}\, \mathrm d x $$	2
935	$$ \displaystyle\int \sin\left({x}^{2}\right){\cdot}\cos\left({x}^{3}\right)\, \mathrm d x $$	2
936	$$ \displaystyle\int \sin\left(x\right){\cdot}\cos\left({x}^{3}\right)\, \mathrm d x $$	2
937	$$ \displaystyle\int \sin\left(\color{orangered}{\square}\right)\, \mathrm d x $$	2
938	$$ \displaystyle\int \dfrac{{x}^{7}}{x+1}\, \mathrm d x $$	2
939	$$ \displaystyle\int^{4}_{0} \dfrac{{x}^{\frac{3}{2}}}{x+1}\, \mathrm d x $$	2
940	$$ \displaystyle\int \sqrt{\dfrac{1+9{x}^{4}}{{x}^{3}-1}}\, \mathrm d x $$	2
941	$$ \displaystyle\int 2x-3\, \mathrm d x $$	2
942	$$ \displaystyle\int \dfrac{{\mathrm{e}}^{x}}{{\left(1-x\right)}^{2}}\, \mathrm d x $$	2
943	$$ \displaystyle\int^{2}_{0} x+6-{x}^{2}+4x-6\, \mathrm d x $$	2
944	$$ 3 $$	2
945	$$ \displaystyle\int \ln\left(\sin\left(x\right)\right)\, \mathrm d x $$	2
946	$$ \displaystyle\int \ln\left(\sin\left(x\sqrtight)\sqrtight)\, \mathsqrtm d x $$	2
947	$$ \displaystyle\int \sqrt{x}\, \mathrm d x $$	2
948	$$ \displaystyle\int^{\infty}_{-\infty} \dfrac{1}{{x}^{2}+2x+5}\, \mathrm d x $$	2
949	$$ \displaystyle\int \dfrac{1}{{x}^{5}}\, \mathrm d x $$	2
950	$$ \displaystyle\int \dfrac{x}{{\left(\sqrt{x}\right)}^{2}+4}\, \mathrm d x $$	2