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Beliebt Rechnen >

integral from 0 to 6x^2 of (t/(t+36))

Lösung

\int_{0}^{6 x^{2}} (\frac{t}{t + 36}) d t

Lösung

6 x^{2} - 36 (ln 6 x^{2} + 36 - 2 ln (6))

Schritte zur Lösung

\int_{0}^{6 x^{2}} \frac{t}{t + 36} d t

Wende U-Substitution an

= \int_{36}^{6 x^{2} + 36} \frac{u - 36}{u} d u

Multipliziere aus

\frac{u - 36}{u} : 1 - \frac{36}{u}

= \int_{36}^{6 x^{2} + 36} 1 - \frac{36}{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

= \int_{36}^{6 x^{2} + 36} 1 d u - \int_{36}^{6 x^{2} + 36} \frac{36}{u} d u

\int_{36}^{6 x^{2} + 36} 1 d u = 6 x^{2}

\int_{36}^{6 x^{2} + 36} \frac{36}{u} d u = 36 (ln 6 x^{2} + 36 - 2 ln (6))

= 6 x^{2} - 36 (ln 6 x^{2} + 36 - 2 ln (6))

Beliebte Beispiele

derivative of 20-x

\frac{d}{d x} (20 - x)

integral of x^{6/7}

\int x^{\frac{6}{7}} d x

derivative 5x(sin(x)+cos(x))

d er i v a t i v e 5 x (sin (x) + cos (x))

d/(dθ)(2sin(2θ))

\frac{d}{d θ} (2 sin (2 θ))

tangent f(x)=6+5x^2-2x^3,\at x=1

t an g e n t f (x) = 6 + 5 x^{2} - 2 x^{3}, at x = 1