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受欢迎的微积分 >

integral of a/(cos^2(bx))

解答

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

解答

a \frac{1}{b} tan (b x) + C

求解步骤

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

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= a \cdot \int \frac{1}{cos ^{2} ( b x )} d x

使用基本三角恒等式:

\frac{1}{cos ( x )} = sec (x)

= a \cdot \int sec^{2} (b x) d x

使用换元积分法

= a \cdot \int \frac{sec ^{2} ( u )}{b} d u

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= a \frac{1}{b} \cdot \int sec^{2} (u) d u

使用积分常见定则:

\int sec^{2} (u) d u = tan (u)

= a \frac{1}{b} tan (u)

u = b x

代回

= a \frac{1}{b} tan (b x)

解答补常数

= a \frac{1}{b} tan (b x) + C

作图

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

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

integral of (5e^{-3+ln(3x)})/x

\int \frac{5 e ^{- 3 + l n (3 x)}}{x} d x

integral of x(1-x^2)^{-1/2}

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