Evaluate
\frac{\pi \left(\pi +2\right)}{2}\approx 8.076394854
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\int x+1\mathrm{d}x
Evaluate the indefinite integral first.
\int x\mathrm{d}x+\int 1\mathrm{d}x
Integrate the sum term by term.
\frac{x^{2}}{2}+\int 1\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}.
\frac{x^{2}}{2}+x
Find the integral of 1 using the table of common integrals rule \int a\mathrm{d}x=ax.
\frac{\pi ^{2}}{2}+\pi -\left(\frac{0^{2}}{2}+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.
\frac{\pi \left(\pi +2\right)}{2}
Simplify.
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Matrix
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Simultaneous equation
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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