integral of x/(cos^2(2x))

解答

\int \frac{x}{cos ^{2} ( 2 x )} d x

\frac{1}{2} x tan (2 x) + \frac{1}{4} ln ∣ cos (2 x) ∣ + C

求解步骤

\int \frac{x}{cos ^{2} ( 2 x )} d x

使用分布积分法

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

\int \frac{1}{2} tan (2 x) d x = - \frac{1}{4} ln ∣ cos (2 x) ∣

= \frac{1}{2} x tan (2 x) - (- \frac{1}{4} ln ∣ cos (2 x) ∣)

化简

= \frac{1}{2} x tan (2 x) + \frac{1}{4} ln ∣ cos (2 x) ∣

解答补常数

= \frac{1}{2} x tan (2 x) + \frac{1}{4} ln ∣ cos (2 x) ∣ + C

\int \frac{3}{( x ^{2} + 2 )} d x

\int \frac{x}{a + 2 x} d x

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

\int y^{2} 4 - y d y

\int x cos^{2} (2 x^{2}) sin (2 x^{2}) d x