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受欢迎的微积分 >

integral of 2tcos(t^2)

解答

\int 2 t cos (t^{2}) d t

解答

sin (t^{2}) + C

求解步骤

\int 2 t cos (t^{2}) d t

提出常数:

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

= 2 \cdot \int t cos (t^{2}) d t

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 = t^{2}

代回

= 2 \cdot \frac{1}{2} sin (t^{2})

化简

2 \cdot \frac{1}{2} sin (t^{2}) : sin (t^{2})

= sin (t^{2})

解答补常数

= sin (t^{2}) + C

作图

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