integral from 3 to sqrt(x of)(t^2+1)

Lösung

\int_{3}^{x} (t^{2} + 1) d t

x + \frac{x ^{\frac{3}{2}}}{3} - 12

Schritte zur Lösung

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

Wende die Summenregel an:

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

= \int_{3}^{x} t^{2} d t + \int_{3}^{x} 1 d t

\int_{3}^{x} t^{2} d t = \frac{x ^{\frac{3}{2}}}{3} - 9

\int_{3}^{x} 1 d t = x - 3

= \frac{x ^{\frac{3}{2}}}{3} - 9 + x - 3

Vereinfache

= x + \frac{x ^{\frac{3}{2}}}{3} - 12

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

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

\int_{0}^{\frac{1}{15}} x ln (15 x) d x

\int_{0}^{1} \frac{1}{( x - 2 ) ( x + 1 )} d x

\int_{x^{2}}^{2 x} x^{2} + y^{2} d y