Integrals – Solved Problems Database

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

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ID	Problem	Count
101	$$ \displaystyle\int \dfrac{1}{x}\, \mathrm d x $$	3
102	$$ \displaystyle\int^{3\pi/2}_{\pi} \left(2x-3\right){\cdot}\sin\left(2x\right)\, \mathrm d x $$	3
103	$$ $$	3
104	$$ \displaystyle\int x{\cdot}{\left(1-x\right)}^{6}\, \mathrm d x $$	3
105	$$ \displaystyle\int^{\pi/2}_{0} {\left(\sin\left(2x\right)\right)}^{2}{\cdot}\cos\left(2x\right)\, \mathrm d x $$	3
106	$$ $$	3
107	$$ \displaystyle\int^{2}_{0} 3{\cdot}\sin\left(x\right)\, \mathrm d x $$	3
108	$$ \displaystyle\int \dfrac{1}{\sqrt{{a}^{2}+{x}^{2}}}\, \mathrm d x $$	3
109	$$ \displaystyle\int \sin\left(x\right)\, \mathrm d x $$	3
110	$$ \displaystyle\int \cos\left(x\right)\, \mathrm d x $$	3
111	$$ \displaystyle\int^{1}_{-1} {x}^{4}-3{x}^{2}+5\, \mathrm d x $$	3
112	$$ \displaystyle\int^{\pi/80}_{0} \dfrac{1}{2}{\cdot}0.0000006{\cdot}{\left(40{\cdot}\mathrm{e}^{-15000t}{\cdot}\sin\left(30000t\right)\right)}^{2}\, \mathrm d x $$	3
113	$$ $$	3
114	$$ \displaystyle\int \dfrac{4x}{\left(x-1\right){\cdot}\left({x}^{2}+x+2\right)}\, \mathrm d x $$	3
115	$$ \displaystyle\int \sqrt{x{\cdot}\left(4-x\right)}\, \mathrm d x $$	3
116	$$ \displaystyle\int {\left(2{x}^{6}-8x-7\right)}^{-2}\, \mathrm d x $$	3
117	$$ \displaystyle\int \sqrt{1+6x+{\left(\dfrac{1}{2{x}^{0.5}}\right)}^{2}}\, \mathrm d x $$	2
118	$$ \displaystyle\int \dfrac{2{t}^{3}}{\sqrt{{t}^{4}-8}}\, \mathrm d x $$	2
119	$$ $$	2
120	$$ \displaystyle\int^{\infty}_{0} \dfrac{\sqrt{x}}{\left(x+1\right){\cdot}\left(x+2\right){\cdot}\left(x+3\right)}\, \mathrm d x $$	2
121	$$ \displaystyle\int \dfrac{1}{5}-2x\, \mathrm d x $$	2
122	$$ \displaystyle\int^{5}_{4} \dfrac{2{t}^{3}}{\sqrt{{t}^{4}-8}}\, \mathrm d x $$	2
123	$$ $$	2
124	$$ \displaystyle\int {\left(1+{x}^{3}\right)}^{n}{\cdot}{x}^{4}\, \mathrm d x $$	2
125	$$ \displaystyle\int \dfrac{20}{4-{x}^{0.5}}\, \mathrm d x $$	2
126	$$ \displaystyle\int \sin\left(\color{orangered}{\square}\right)\, \mathrm d x $$	2
127	$$ \displaystyle\int \dfrac{2}{3}{\cdot}{x}^{2}{\cdot}\ln\left({x}^{3}\right)\, \mathrm d x $$	2
128	$$ \displaystyle\int {\left(1+{x}^{3}\right)}^{2}{\cdot}{x}^{4}\, \mathrm d x $$	2
129	$$ \displaystyle\int^{81}_{25} \dfrac{\sqrt{x}}{x-4}\, \mathrm d x $$	2
130	$$ $$	2
131	$$ $$	2
132	$$ \int^{\pi/2}_{-\pi/2} \frac{{1}}{{\cos{{\left(\frac{{x}}{{2}}\right)}}}} \, d\,x $$	2
133	$$ \displaystyle\int \dfrac{\cos\left(5x\right)}{{\mathrm{e}}^{x}}\, \mathrm d x $$	2
134	$$ \displaystyle\int {\left(\cos\left(x\right)\right)}^{2}\, \mathrm d x $$	2
135	$$ \displaystyle\int \dfrac{{x}^{2}+2x+1}{{x}^{3}}\, \mathrm d x $$	2
136	$$ \displaystyle\int^{64}_{25} \dfrac{\sqrt{x}}{x-4}\, \mathrm d x $$	2
137	$$ \displaystyle\int^{3}_{-6} 3-\dfrac{{x}^{2}}{4}-x\, \mathrm d x $$	2
138	$$ $$	2
139	$$ \displaystyle\int^{3}_{1} {x}^{3}{\cdot}\sqrt{x+2}\, \mathrm d x $$	2
140	$$ $$	2
141	$$ \displaystyle\int -{\mathrm{e}}^{x}{\cdot}\sqrt{9{\mathrm{e}}^{2x}+4}\, \mathrm d x $$	2
142	$$ $$	2
143	$$ \displaystyle\int \dfrac{1}{{\left(\sin\left(x\right)\right)}^{3}}\, \mathrm d x $$	2
144	$$ \displaystyle\int \dfrac{7}{x}{\cdot}\sqrt{16{x}^{2}-64}\, \mathrm d x $$	2
145	$$ \displaystyle\int \left(x+1\right){\cdot}\sqrt{2-x}\, \mathrm d x $$	2
146	$$ $$	2
147	$$ \displaystyle\int {x}^{3}{\cdot}{\left(3+4{x}^{3}\right)}^{8}\, \mathrm d x $$	2
148	$$ \displaystyle\int \dfrac{-12{x}^{3}}{\ln\left(1-x\right)}\, \mathrm d x $$	2
149	$$ \displaystyle\int^{3.25789}_{0} \dfrac{{x}^{4}-10{x}^{2}-2x}{2{x}^{2}+1}\, \mathrm d x $$	2
150	$$ \displaystyle\int^{1}_{0} \sqrt{\sqrt{x}-x}\, \mathrm d x $$	2