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Integral dari $$$x^{3} \sqrt{x^{21}}$$$
Kalkulator terkait: Kalkulator Integral Tentu dan Tak Wajar
Masukan Anda
Temukan $$$\int x^{3} \sqrt{x^{21}}\, dx$$$.
Solusi
Masukan ditulis ulang: $$$\int{x^{3} \sqrt{x^{21}} d x}=\int{x^{\frac{27}{2}} d x}$$$.
Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=\frac{27}{2}$$$:
$${\color{red}{\int{x^{\frac{27}{2}} d x}}}={\color{red}{\frac{x^{1 + \frac{27}{2}}}{1 + \frac{27}{2}}}}={\color{red}{\left(\frac{2 x^{\frac{29}{2}}}{29}\right)}}$$
Oleh karena itu,
$$\int{x^{\frac{27}{2}} d x} = \frac{2 x^{\frac{29}{2}}}{29}$$
Tambahkan konstanta integrasi:
$$\int{x^{\frac{27}{2}} d x} = \frac{2 x^{\frac{29}{2}}}{29}+C$$
Jawaban
$$$\int x^{3} \sqrt{x^{21}}\, dx = \frac{2 x^{\frac{29}{2}}}{29} + C$$$A