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Integral dari $$$- \frac{1}{\sqrt{1 - x^{2}}}$$$
Kalkulator terkait: Kalkulator Integral Tentu dan Tak Wajar
Masukan Anda
Temukan $$$\int \left(- \frac{1}{\sqrt{1 - x^{2}}}\right)\, dx$$$.
Solusi
Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=-1$$$ dan $$$f{\left(x \right)} = \frac{1}{\sqrt{1 - x^{2}}}$$$:
$${\color{red}{\int{\left(- \frac{1}{\sqrt{1 - x^{2}}}\right)d x}}} = {\color{red}{\left(- \int{\frac{1}{\sqrt{1 - x^{2}}} d x}\right)}}$$
Integral dari $$$\frac{1}{\sqrt{1 - x^{2}}}$$$ adalah $$$\int{\frac{1}{\sqrt{1 - x^{2}}} d x} = \operatorname{asin}{\left(x \right)}$$$:
$$- {\color{red}{\int{\frac{1}{\sqrt{1 - x^{2}}} d x}}} = - {\color{red}{\operatorname{asin}{\left(x \right)}}}$$
Oleh karena itu,
$$\int{\left(- \frac{1}{\sqrt{1 - x^{2}}}\right)d x} = - \operatorname{asin}{\left(x \right)}$$
Tambahkan konstanta integrasi:
$$\int{\left(- \frac{1}{\sqrt{1 - x^{2}}}\right)d x} = - \operatorname{asin}{\left(x \right)}+C$$
Jawaban
$$$\int \left(- \frac{1}{\sqrt{1 - x^{2}}}\right)\, dx = - \operatorname{asin}{\left(x \right)} + C$$$A