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1 |
`int0dx=C`
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2 |
`intdx=x+C`
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3 |
`intx^{alpha}dx={x^{alpha+1}}/{alpha+1}+C (alpha!=-1, alpha in RR)`
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4 |
`int{dx}/x=ln|x|+C (alpha=-1)`
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5 |
`int{dx}/sqrt(x)=2sqrt(x)+C`
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6 |
`inte^xdx=e^x+C`
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7 |
`inta^xdx={a^x}/{lna}+C`
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8 |
`intcosxdx=sinx+C`
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9 |
`intsinxdx=-cosx+C`
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10 |
`int{dx}/{cos^2x}=tgx+C`
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11 |
`int{dx}/{sin^2x}=-ctgx+C`
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12 |
`int{dx}/sqrt(a^2-x^2)=arc sin (x/a)+C`
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13 |
`int{dx}/{a^2+x^2}=1/a arc tg (x/a)+C`
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14 |
`int{dx}/sqrt(x^2+-a^2)=ln|x+sqrt(x^2+-a^2)|+C`
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15 |
`int{dx}/{x^2-a^2}=1/{2a}ln|(x-a}/{x+a}|+C`
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16 |
`inttgxdx=-ln|cosx|+C`
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17 |
`int ctgxdx=ln|sinx|+C`
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