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受欢迎的微积分 >

integral of (2x+4)cos(x^2+4x-6)

解答

\int (2 x + 4) cos (x^{2} + 4 x - 6) d x

解答

sin (x^{2} + 4 x - 6) + C

求解步骤

\int (2 x + 4) cos (x^{2} + 4 x - 6) d x

(2 x + 4) cos (x^{2} + 4 x - 6) = 2 (x + 2) cos (x^{2} + 4 x - 6)

= \int 2 (x + 2) cos (x^{2} + 4 x - 6) d x

提出常数:

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

= 2 \cdot \int (x + 2) cos (x^{2} + 4 x - 6) d x

使用换元积分法

= 2 \cdot \int \frac{cos ( u )}{2} d u

提出常数:

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

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

使用积分常见定则:

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

= 2 \cdot \frac{1}{2} sin (u)

u = x^{2} + 4 x - 6

代回

= 2 \cdot \frac{1}{2} sin (x^{2} + 4 x - 6)

化简

2 \cdot \frac{1}{2} sin (x^{2} + 4 x - 6) : sin (x^{2} + 4 x - 6)

= sin (x^{2} + 4 x - 6)

解答补常数

= sin (x^{2} + 4 x - 6) + C

作图

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