integral cos^2(x)

الحلّ

integral

cos^{2} (x)

\frac{1}{2} (x + \frac{1}{2} sin (2 x)) + C

خطوات الحلّ

\int cos^{2} (x) d x

Rewrite using trig identities

= \int \frac{1 + cos ( 2 x )}{2} d x

\int a \cdot f (x) d x = a \cdot \int f (x) d x

:قم بإخراج الثابت

= \frac{1}{2} \cdot \int 1 + cos (2 x) d x

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

:فعّل الميزة الخطيّة

= \frac{1}{2} (\int 1 d x + \int cos (2 x) d x)

\int 1 d x = x

\int cos (2 x) d x = \frac{1}{2} sin (2 x)

= \frac{1}{2} (x + \frac{1}{2} sin (2 x))

أضف ثابت التكامل للحل

= \frac{1}{2} (x + \frac{1}{2} sin (2 x)) + C

f (x) = 3 x^{2}

(42, 42)

(- 6, 0)

3 x^{3}

2 + x = 6