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144
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\int x^{2}-6x+5\mathrm{d}x
Evaluate the indefinite integral first.
\int x^{2}\mathrm{d}x+\int -6x\mathrm{d}x+\int 5\mathrm{d}x
Integrate the sum term by term.
\int x^{2}\mathrm{d}x-6\int x\mathrm{d}x+\int 5\mathrm{d}x
Factor out the constant in each of the terms.
\frac{x^{3}}{3}-6\int x\mathrm{d}x+\int 5\mathrm{d}x
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{2}\mathrm{d}x with \frac{x^{3}}{3}.
\frac{x^{3}}{3}-3x^{2}+\int 5\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}. اضرب -6 في \frac{x^{2}}{2}.
\frac{x^{3}}{3}-3x^{2}+5x
Find the integral of 5 using the table of common integrals rule \int a\mathrm{d}x=ax.
\frac{1^{3}}{3}-3\times 1^{2}+5\times 1-\left(\frac{\left(-5\right)^{3}}{3}-3\left(-5\right)^{2}+5\left(-5\right)\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.
144
تبسيط.
أمثلة
معادلة تربيعية
{ x } ^ { 2 } - 4 x - 5 = 0
حساب المثلثات
4 \sin \theta \cos \theta = 2 \sin \theta
معادلة خطية
y = 3x + 4
الحساب
699 * 533
المصفوفة
\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]
معادلة آنية
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
التفاضل
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
التكامل
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
النهايات
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}