integral of x^5-pi^5+x^2-pi^2

الحلّ

\int x^{5} - π^{5} + x^{2} - π^{2} d x

\frac{x ^{6}}{6} - π^{5} x + \frac{x ^{3}}{3} - π^{2} x + C

خطوات الحلّ

\int x^{5} - π^{5} + x^{2} - π^{2} d x

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

:فعّل الميزة الخطيّة

= \int x^{5} d x - \int π^{5} d x + \int x^{2} d x - \int π^{2} d x

\int x^{5} d x = \frac{x ^{6}}{6}

\int π^{5} d x = π^{5} x

\int x^{2} d x = \frac{x ^{3}}{3}

\int π^{2} d x = π^{2} x

= \frac{x ^{6}}{6} - π^{5} x + \frac{x ^{3}}{3} - π^{2} x

أضف ثابت التكامل للحل

= \frac{x ^{6}}{6} - π^{5} x + \frac{x ^{3}}{3} - π^{2} x + C

\int (a x^{6} + b x^{4} + 3 c) d x

\int cos (x) e^{x} d x

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\int \frac{1}{3 y ^{2}} d y

\int 5 (x^{2} - 5 x - 2) d x