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Klipbordga nusxa olish
\int \frac{\frac{1}{6}+\frac{3}{6}}{2-\frac{1}{3}}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x
6 va 2 ning eng kichik umumiy karralisi 6 ga teng. \frac{1}{6} va \frac{1}{2} ni 6 maxraj bilan kasrlarga aylantirib oling.
\int \frac{\frac{1+3}{6}}{2-\frac{1}{3}}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x
\frac{1}{6} va \frac{3}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.
\int \frac{\frac{4}{6}}{2-\frac{1}{3}}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x
4 olish uchun 1 va 3'ni qo'shing.
\int \frac{\frac{2}{3}}{2-\frac{1}{3}}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x
\frac{4}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.
\int \frac{\frac{2}{3}}{\frac{6}{3}-\frac{1}{3}}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x
2 ni \frac{6}{3} kasrga o‘giring.
\int \frac{\frac{2}{3}}{\frac{6-1}{3}}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x
\frac{6}{3} va \frac{1}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.
\int \frac{\frac{2}{3}}{\frac{5}{3}}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x
5 olish uchun 6 dan 1 ni ayirish.
\int \frac{2}{3}\times \frac{3}{5}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x
\frac{2}{3} ni \frac{5}{3} ga bo'lish \frac{2}{3} ga k'paytirish \frac{5}{3} ga qaytarish.
\int \frac{2\times 3}{3\times 5}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x
Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{2}{3} ni \frac{3}{5} ga ko‘paytiring.
\int \frac{2}{5}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x
Surat va maxrajdagi ikkala 3 ni qisqartiring.
\int \frac{2}{5}-\left(\frac{3}{6}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x
2 va 6 ning eng kichik umumiy karralisi 6 ga teng. \frac{1}{2} va \frac{1}{6} ni 6 maxraj bilan kasrlarga aylantirib oling.
\int \frac{2}{5}-\frac{3-1}{6}\times \frac{6}{5}\mathrm{d}x
\frac{3}{6} va \frac{1}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.
\int \frac{2}{5}-\frac{2}{6}\times \frac{6}{5}\mathrm{d}x
2 olish uchun 3 dan 1 ni ayirish.
\int \frac{2}{5}-\frac{1}{3}\times \frac{6}{5}\mathrm{d}x
\frac{2}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.
\int \frac{2}{5}-\frac{1\times 6}{3\times 5}\mathrm{d}x
Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{3} ni \frac{6}{5} ga ko‘paytiring.
\int \frac{2}{5}-\frac{6}{15}\mathrm{d}x
\frac{1\times 6}{3\times 5} kasridagi ko‘paytirishlarni bajaring.
\int \frac{2}{5}-\frac{2}{5}\mathrm{d}x
\frac{6}{15} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.
\int 0\mathrm{d}x
0 olish uchun \frac{2}{5} dan \frac{2}{5} ni ayirish.
0
\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 0 integralini toping.
С
Агар F\left(x\right)f\left(x\right) ning dastlabki holati boʻlsa, u holatda f\left(x\right) ning barcha dastlabki holatlari toʻplami F\left(x\right)+C tarafidan belgilanadi. Shu sababli natijaga C\in \mathrm{R} integrallash konstantasini qoʻshing.
Misollar
Ikkilik tenglama
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometriya
4 \sin \theta \cos \theta = 2 \sin \theta
Chiziqli tenglama
y = 3x + 4
Arifmetik
699 * 533
Matritsa
\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]
Simli tenglama
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differensatsiya
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Oʻngga
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Chegaralar
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}