integral of (tsqrt(t)+sqrt(t))/(t^2)

Lösung

\int \frac{t t + t}{t ^{2}} d t

2 t - \frac{2}{t} + C

Schritte zur Lösung

\int \frac{t t + t}{t ^{2}} d t

\frac{t t + t}{t ^{2}} = (\frac{t t}{t ^{2}} + \frac{t}{t ^{2}})

= \int \frac{t t}{t ^{2}} + \frac{t}{t ^{2}} d t

Vereinfache

\frac{t t}{t ^{2}} + \frac{t}{t ^{2}} : \frac{1}{t} + \frac{1}{t ^{\frac{3}{2}}}

= \int \frac{1}{t} + \frac{1}{t ^{\frac{3}{2}}} 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 \frac{1}{t} d t + \int \frac{1}{t ^{\frac{3}{2}}} d t

\int \frac{1}{t} d t = 2 t

\int \frac{1}{t ^{\frac{3}{2}}} d t = - \frac{2}{t}

= 2 t - \frac{2}{t}

Füge eine Konstante zur Lösung hinzu

= 2 t - \frac{2}{t} + C

R (a) = (3 a + 1)^{2}

y^{^{'}} + 4 y = t^{2} e^{- 4 t}

\int \frac{2 x + 7}{9 - 4 x ^{2}} d x

\int_{6}^{8} \frac{60}{( x - 6 ) ^{3}} d x

t an g e n t y = ln (x), at x = 2