de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 2 to x^2 of cos(x^2+1)

Lösung

\int_{2}^{x^{2}} cos (x^{2} + 1) d x

Lösung

cos (1) (\frac{π}{2} C (\frac{2}{π} x^{2}) - \frac{π}{2} C (\frac{2}{π} \cdot 2)) - sin (1) (\frac{π}{2} § (\frac{2}{π} x^{2}) - \frac{π}{2} § (\frac{2}{π} \cdot 2))

Schritte zur Lösung

\int_{2}^{x^{2}} cos (x^{2} + 1) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{2}^{x^{2}} cos (x^{2}) cos (1) - sin (x^{2}) sin (1) d x

Wende die Summenregel an:

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

= \int_{2}^{x^{2}} cos (x^{2}) cos (1) d x - \int_{2}^{x^{2}} sin (x^{2}) sin (1) d x

\int_{2}^{x^{2}} cos (x^{2}) cos (1) d x = cos (1) (\frac{π}{2} C (\frac{2}{π} x^{2}) - \frac{π}{2} C (\frac{2}{π} \cdot 2))

\int_{2}^{x^{2}} sin (x^{2}) sin (1) d x = sin (1) (\frac{π}{2} § (\frac{2}{π} x^{2}) - \frac{π}{2} § (\frac{2}{π} \cdot 2))

= cos (1) (\frac{π}{2} C (\frac{2}{π} x^{2}) - \frac{π}{2} C (\frac{2}{π} \cdot 2)) - sin (1) (\frac{π}{2} § (\frac{2}{π} x^{2}) - \frac{π}{2} § (\frac{2}{π} \cdot 2))

Beliebte Beispiele

integral from 0 to 2pi of x^2sin(2x)

\int_{0}^{2 π} x^{2} sin (2 x) d x

d/(dt)(3sin(3t))

\frac{d}{d t} (3 sin (3 t))

((2y)/x+2x)+(2ln(x)-3)y^'=0

(\frac{2 y}{x} + 2 x) + (2 ln (x) - 3) y^{^{'}} = 0

(\partial)/(\partial x)((26x^2)/((x-y)^2))

\frac{\partial}{\partial x} (\frac{26 x ^{2}}{( x - y ) ^{2}})

tangent 1+4x^2-2x^3

t an g e n t 1 + 4 x^{2} - 2 x^{3}