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\int 2x-2\mathrm{d}x
Evaluate the indefinite integral first.
\int 2x\mathrm{d}x+\int -2\mathrm{d}x
Integrate the sum term by term.
2\int x\mathrm{d}x+\int -2\mathrm{d}x
Factor out the constant in each of the terms.
x^{2}+\int -2\mathrm{d}x
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}. Multiply 2 times \frac{x^{2}}{2}.
x^{2}-2x
Find the integral of -2 using the table of common integrals rule \int a\mathrm{d}x=ax.
5^{2}-2\times 5-\left(0^{2}-2\times 0\right)
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
15
Simplify.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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