គណនាអាំងតេក្រាលនៃ (a+bx^3)^2

គណនា

$\int{\left(a+bx^3\right)^2 \mathrm{d}x}$

ចម្លើយ

$\int{\left(a+bx^3\right)^2 \mathrm{d}x}=\int(a^2+2abx^3+b^2 x^6 )\mathrm{d}x$
$=a^2 \int \mathrm{d}x+2ab\int x^3 \mathrm{d}x+b^2 \int x^6 \mathrm{d}x$
$\displaystyle =a^2 x+2ab\left(\frac{1}{4} x^4\right)+b^2 \left(\frac{1}{7} x^7 \right)+C$
$\displaystyle =a^2 x+\frac{1}{2} abx^4+\frac{1}{7} b^2 x^7+C$