integral from 0 to 3 of xsqrt(1+2x)

Lösung

\int_{0}^{3} x 1 + 2 x d x

\frac{56 7 + 1}{15}

Dezimale

9.94413 \dots

Schritte zur Lösung

\int_{0}^{3} x 1 + 2 x d x

Wende U-Substitution an

= \int_{1}^{7} \frac{u ( u - 1 )}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{1}^{7} u (u - 1) d u

Multipliziere aus

u (u - 1) : u^{\frac{3}{2}} - u

= \frac{1}{4} \cdot \int_{1}^{7} u^{\frac{3}{2}} - u d u

Wende die Summenregel an:

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

= \frac{1}{4} (\int_{1}^{7} u^{\frac{3}{2}} d u - \int_{1}^{7} u d u)

\int_{1}^{7} u^{\frac{3}{2}} d u = \frac{98 7 - 2}{5}

\int_{1}^{7} u d u = \frac{14 7 - 2}{3}

= \frac{1}{4} (\frac{98 7 - 2}{5} - \frac{14 7 - 2}{3})

Vereinfache

\frac{1}{4} (\frac{98 7 - 2}{5} - \frac{14 7 - 2}{3}) : \frac{56 7 + 1}{15}

= \frac{56 7 + 1}{15}

\int (y^{2} + ln (x)) d y

\int_{0}^{5} 7 x - x^{2} - 2 x d x

x \to 0 lim (sec (x))

\int \frac{x ^{4} + 2 x + 1}{x ^{3} - x ^{2} - 2 x} d x

d er i v a t i v e f (x) = e^{e x}