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Beliebt Rechnen >

integral of xsec^2(4x)

Lösung

\int x sec^{2} (4 x) d x

Lösung

\frac{1}{2} x^{2} sec^{2} (4 x) - \frac{1}{16} (8 x^{2} tan^{2} (4 x) - 4 x tan (4 x) - ln ∣ cos (4 x) ∣ + 8 x^{2}) + C

Schritte zur Lösung

\int x sec^{2} (4 x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int x (1 + tan^{2} (4 x)) d x

Wende die partielle Integration an

= \frac{1}{2} x^{2} sec^{2} (4 x) - \int 4 x^{2} sec^{2} (4 x) tan (4 x) d x

\int 4 x^{2} sec^{2} (4 x) tan (4 x) d x = \frac{1}{16} (8 x^{2} tan^{2} (4 x) - 4 x tan (4 x) - ln ∣ cos (4 x) ∣ + 8 x^{2})

= \frac{1}{2} x^{2} sec^{2} (4 x) - \frac{1}{16} (8 x^{2} tan^{2} (4 x) - 4 x tan (4 x) - ln ∣ cos (4 x) ∣ + 8 x^{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{2} sec^{2} (4 x) - \frac{1}{16} (8 x^{2} tan^{2} (4 x) - 4 x tan (4 x) - ln ∣ cos (4 x) ∣ + 8 x^{2}) + C

Graph

Beliebte Beispiele

tangent f(x)=(x^2-15)^7,\at x=4

t an g e n t f (x) = (x^{2} - 15)^{7}, at x = 4

x(dy)/(dx)+2y=6x^2sqrt(y)

x \frac{d y}{d x} + 2 y = 6 x^{2} y

derivative of acos^3(x)

\frac{d}{d x} (a cos^{3} (x))

derivative y=x^2ln(3x)

d er i v a t i v e y = x^{2} ln (3 x)

y^'=((1-y)^2)/(x+1),y(0)=5

y^{^{'}} = \frac{( 1 - y ) ^{2}}{x + 1}, y (0) = 5