$$$x$$$ değişkenine göre $$$- 4 \sqrt{30} x^{2} \sqrt{i n t} - x^{2} + 880$$$ fonksiyonunun integrali

Bulun: $$$\int \left(- 4 \sqrt{30} x^{2} \sqrt{i n t} - x^{2} + 880\right)\, dx$$$.

Girdi yeniden yazıldı: $$$\int{\left(- 4 \sqrt{30} x^{2} \sqrt{i n t} - x^{2} + 880\right)d x}=\int{\left(- 4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} x^{2} - x^{2} + 880\right)d x}$$$.

Her terimin integralini alın:

$${\color{red}{\int{\left(- 4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} x^{2} - x^{2} + 880\right)d x}}} = {\color{red}{\left(\int{880 d x} - \int{x^{2} d x} - \int{4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} x^{2} d x}\right)}}$$

$$$c=880$$$ kullanarak $$$\int c\, dx = c x$$$ sabit kuralını uygula:

$$- \int{x^{2} d x} - \int{4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} x^{2} d x} + {\color{red}{\int{880 d x}}} = - \int{x^{2} d x} - \int{4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} x^{2} d x} + {\color{red}{\left(880 x\right)}}$$

Kuvvet kuralını $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ $$$n=2$$$ ile uygulayın:

$$880 x - \int{4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} x^{2} d x} - {\color{red}{\int{x^{2} d x}}}=880 x - \int{4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} x^{2} d x} - {\color{red}{\frac{x^{1 + 2}}{1 + 2}}}=880 x - \int{4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} x^{2} d x} - {\color{red}{\left(\frac{x^{3}}{3}\right)}}$$

Sabit katsayı kuralı $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$'i $$$c=4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t}$$$ ve $$$f{\left(x \right)} = x^{2}$$$ ile uygula:

$$- \frac{x^{3}}{3} + 880 x - {\color{red}{\int{4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} x^{2} d x}}} = - \frac{x^{3}}{3} + 880 x - {\color{red}{\left(4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} \int{x^{2} d x}\right)}}$$

Kuvvet kuralını $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ $$$n=2$$$ ile uygulayın:

$$- 4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} {\color{red}{\int{x^{2} d x}}} - \frac{x^{3}}{3} + 880 x=- 4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} {\color{red}{\frac{x^{1 + 2}}{1 + 2}}} - \frac{x^{3}}{3} + 880 x=- 4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} {\color{red}{\left(\frac{x^{3}}{3}\right)}} - \frac{x^{3}}{3} + 880 x$$

Dolayısıyla,

$$\int{\left(- 4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} x^{2} - x^{2} + 880\right)d x} = - \frac{4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} x^{3}}{3} - \frac{x^{3}}{3} + 880 x$$

Sadeleştirin:

$$\int{\left(- 4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} x^{2} - x^{2} + 880\right)d x} = \frac{x \left(- 4 \sqrt{15} \sqrt{n} \sqrt{t} x^{2} \left(1 + i\right) - x^{2} + 2640\right)}{3}$$

İntegrasyon sabitini ekleyin:

$$\int{\left(- 4 \sqrt{30} \sqrt{i} \sqrt{n} \sqrt{t} x^{2} - x^{2} + 880\right)d x} = \frac{x \left(- 4 \sqrt{15} \sqrt{n} \sqrt{t} x^{2} \left(1 + i\right) - x^{2} + 2640\right)}{3}+C$$

$$$\int \left(- 4 \sqrt{30} x^{2} \sqrt{i n t} - x^{2} + 880\right)\, dx = \frac{x \left(- 4 \sqrt{15} \sqrt{n} \sqrt{t} x^{2} \left(1 + i\right) - x^{2} + 2640\right)}{3} + C$$$A