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受欢迎的微积分 >

integral of 6xsec^2(x^2)cos(tan(x^2))

解答

\int 6 x sec^{2} (x^{2}) cos (tan (x^{2})) d x

解答

3 sin (tan (x^{2})) + C

求解步骤

\int 6 x sec^{2} (x^{2}) cos (tan (x^{2})) d x

提出常数:

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

= 6 \cdot \int x sec^{2} (x^{2}) cos (tan (x^{2})) d x

使用换元积分法

= 6 \cdot \int \frac{sec ^{2} ( u ) cos ( tan ( u ) )}{2} d u

提出常数:

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

= 6 \cdot \frac{1}{2} \cdot \int sec^{2} (u) cos (tan (u)) d u

使用换元积分法

= 6 \cdot \frac{1}{2} \cdot \int cos (v) d v

使用积分常见定则:

\int cos (v) d v = sin (v)

= 6 \cdot \frac{1}{2} sin (v)

代回

= 6 \cdot \frac{1}{2} sin (tan (x^{2}))

化简

6 \cdot \frac{1}{2} sin (tan (x^{2})) : 3 sin (tan (x^{2}))

= 3 sin (tan (x^{2}))

解答补常数

= 3 sin (tan (x^{2})) + C

作图

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