integral of (5x^4)/4+(3x^2)/2+7x+C

Lösung

\int \frac{5 x ^{4}}{4} + \frac{3 x ^{2}}{2} + 7 x + C d x

\frac{x ^{5}}{4} + \frac{x ^{3}}{2} + \frac{7 x ^{2}}{2} + C x + C

Schritte zur Lösung

\int \frac{5 x ^{4}}{4} + \frac{3 x ^{2}}{2} + 7 x + C d x

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{5 x ^{4}}{4} d x + \int \frac{3 x ^{2}}{2} d x + \int 7 x d x + \int C d x

\int \frac{5 x ^{4}}{4} d x = \frac{x ^{5}}{4}

\int \frac{3 x ^{2}}{2} d x = \frac{x ^{3}}{2}

\int 7 x d x = \frac{7 x ^{2}}{2}

\int C d x = C x

= \frac{x ^{5}}{4} + \frac{x ^{3}}{2} + \frac{7 x ^{2}}{2} + C x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{4} + \frac{x ^{3}}{2} + \frac{7 x ^{2}}{2} + C x + C

in v erse l a pl a ce \frac{s + 1}{( s + 1 ) ^{2} + 1}

\int (11 x)^{2} d x

\int \frac{1}{( x + 4 ) ^{\frac{7}{2}}} d x

y^{^{'}} + 2 x y = 1

\frac{\partial}{\partial x} (e^{t})