integral from 0 to sqrt(ln(pi) of)2xe^{x^2}cos(e^{x^2})

Lösung

\int_{0}^{l n (π)} 2 x e^{x^{2}} cos (e^{x^{2}}) d x

- sin (1)

Dezimale

- 0.84147 \dots

Schritte zur Lösung

\int_{0}^{l n (π)} 2 x e^{x^{2}} cos (e^{x^{2}}) d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{l n (π)} x e^{x^{2}} cos (e^{x^{2}}) d x

Wende U-Substitution an

= 2 \cdot \int_{0}^{l n (π)} \frac{e ^{u} cos ( e ^{u} )}{2} d u

Entferne die Konstante:

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

= 2 \cdot \frac{1}{2} \cdot \int_{0}^{l n (π)} e^{u} cos (e^{u}) d u

Wende U-Substitution an

= 2 \cdot \frac{1}{2} \cdot \int_{1}^{π} cos (v) d v

Nutze das gemeinsame Integral :

\int cos (v) d v = sin (v)

= 2 \cdot \frac{1}{2} [sin (v)]_{1}^{π}

Vereinfache

2 \cdot \frac{1}{2} [sin (v)]_{1}^{π} : [sin (v)]_{1}^{π}

= [sin (v)]_{1}^{π}

Berechne die Grenzen:

- sin (1)

= - sin (1)

x \to - 6 - lim (x^{2} + \frac{2}{x + 6})

\frac{\partial}{\partial x} (1 + 2 x)

a re a 9 - x^{2}, x

f (t) = 1 + t^{2}

\int \frac{( 1 - x ) ^{3}}{( x ^{3} x )} d x