integral from 0 to x of t(e^{t^3}-1)

Lösung

\int_{0}^{x} t (e^{t^{3}} - 1) d t

\frac{1}{2} - \frac{x ^{2} Γ ( \frac{1}{\frac{3}{2}} , - ( x ^{2} ) ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - ( x ^{2} ) ^{\frac{3}{2}}} - - \frac{0 \cdot Γ ( \frac{1}{\frac{3}{2}} , - 0 ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - 0 ^{\frac{3}{2}}} - \frac{x ^{2}}{2}

Schritte zur Lösung

\int_{0}^{x} t (e^{t^{3}} - 1) d t

Multipliziere aus

t (e^{t^{3}} - 1) : e^{t^{3}} t - t

= \int_{0}^{x} e^{t^{3}} t - t 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_{0}^{x} e^{t^{3}} t d t - \int_{0}^{x} t d t

\int_{0}^{x} e^{t^{3}} t d t = \frac{1}{2} - \frac{x ^{2} Γ ( \frac{1}{\frac{3}{2}} , - ( x ^{2} ) ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - ( x ^{2} ) ^{\frac{3}{2}}} - - \frac{0 \cdot Γ ( \frac{1}{\frac{3}{2}} , - 0 ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - 0 ^{\frac{3}{2}}}

\int_{0}^{x} t d t = \frac{x ^{2}}{2}

= \frac{1}{2} - \frac{x ^{2} Γ ( \frac{1}{\frac{3}{2}} , - ( x ^{2} ) ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - ( x ^{2} ) ^{\frac{3}{2}}} - - \frac{0 \cdot Γ ( \frac{1}{\frac{3}{2}} , - 0 ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - 0 ^{\frac{3}{2}}} - \frac{x ^{2}}{2}

\int cos^{3} (3 θ) sin^{- 2} (3 θ) d θ

d er i v a t i v e \frac{2 t + 1}{t + 3}

d er i v a t i v e 8 x + 9 x e^{x}

\int cos (\frac{nπ x}{L}) d x

\frac{d}{d x} (3^{2 x^{2}} \cdot x)