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Integral dari $$$\frac{1}{t^{6}}$$$
Kalkulator terkait: Kalkulator Integral Tentu dan Tak Wajar
Masukan Anda
Temukan $$$\int \frac{1}{t^{6}}\, dt$$$.
Solusi
Terapkan aturan pangkat $$$\int t^{n}\, dt = \frac{t^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=-6$$$:
$${\color{red}{\int{\frac{1}{t^{6}} d t}}}={\color{red}{\int{t^{-6} d t}}}={\color{red}{\frac{t^{-6 + 1}}{-6 + 1}}}={\color{red}{\left(- \frac{t^{-5}}{5}\right)}}={\color{red}{\left(- \frac{1}{5 t^{5}}\right)}}$$
Oleh karena itu,
$$\int{\frac{1}{t^{6}} d t} = - \frac{1}{5 t^{5}}$$
Tambahkan konstanta integrasi:
$$\int{\frac{1}{t^{6}} d t} = - \frac{1}{5 t^{5}}+C$$
Jawaban
$$$\int \frac{1}{t^{6}}\, dt = - \frac{1}{5 t^{5}} + C$$$A