$$$- \frac{3 \sqrt{13} \sqrt{x}}{13} + 2$$$'nin integrali

Bulun: $$$\int \left(- \frac{3 \sqrt{13} \sqrt{x}}{13} + 2\right)\, dx$$$.

Her terimin integralini alın:

$${\color{red}{\int{\left(- \frac{3 \sqrt{13} \sqrt{x}}{13} + 2\right)d x}}} = {\color{red}{\left(\int{2 d x} - \int{\frac{3 \sqrt{13} \sqrt{x}}{13} d x}\right)}}$$

$$$c=2$$$ kullanarak $$$\int c\, dx = c x$$$ sabit kuralını uygula:

$$- \int{\frac{3 \sqrt{13} \sqrt{x}}{13} d x} + {\color{red}{\int{2 d x}}} = - \int{\frac{3 \sqrt{13} \sqrt{x}}{13} d x} + {\color{red}{\left(2 x\right)}}$$

Sabit katsayı kuralı $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$'i $$$c=\frac{3 \sqrt{13}}{13}$$$ ve $$$f{\left(x \right)} = \sqrt{x}$$$ ile uygula:

$$2 x - {\color{red}{\int{\frac{3 \sqrt{13} \sqrt{x}}{13} d x}}} = 2 x - {\color{red}{\left(\frac{3 \sqrt{13} \int{\sqrt{x} d x}}{13}\right)}}$$

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

$$2 x - \frac{3 \sqrt{13} {\color{red}{\int{\sqrt{x} d x}}}}{13}=2 x - \frac{3 \sqrt{13} {\color{red}{\int{x^{\frac{1}{2}} d x}}}}{13}=2 x - \frac{3 \sqrt{13} {\color{red}{\frac{x^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}}}}{13}=2 x - \frac{3 \sqrt{13} {\color{red}{\left(\frac{2 x^{\frac{3}{2}}}{3}\right)}}}{13}$$

Dolayısıyla,

$$\int{\left(- \frac{3 \sqrt{13} \sqrt{x}}{13} + 2\right)d x} = - \frac{2 \sqrt{13} x^{\frac{3}{2}}}{13} + 2 x$$

İntegrasyon sabitini ekleyin:

$$\int{\left(- \frac{3 \sqrt{13} \sqrt{x}}{13} + 2\right)d x} = - \frac{2 \sqrt{13} x^{\frac{3}{2}}}{13} + 2 x+C$$

$$$\int \left(- \frac{3 \sqrt{13} \sqrt{x}}{13} + 2\right)\, dx = \left(- \frac{2 \sqrt{13} x^{\frac{3}{2}}}{13} + 2 x\right) + C$$$A