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受欢迎的微积分 >

integral of-9xcos(7x)

解答

\int - 9 x cos (7 x) d x

解答

- \frac{9}{49} (7 x sin (7 x) + cos (7 x)) + C

求解步骤

\int - 9 x cos (7 x) d x

提出常数:

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

= - 9 \cdot \int x cos (7 x) d x

使用换元积分法

= - 9 \cdot \int \frac{u cos ( u )}{49} d u

提出常数:

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

= - 9 \cdot \frac{1}{49} \cdot \int u cos (u) d u

使用分布积分法

= - 9 \cdot \frac{1}{49} (u sin (u) - \int sin (u) d u)

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

= - 9 \cdot \frac{1}{49} (u sin (u) - (- cos (u)))

u = 7 x

代回

= - 9 \cdot \frac{1}{49} (7 x sin (7 x) - (- cos (7 x)))

化简

- 9 \cdot \frac{1}{49} (7 x sin (7 x) - (- cos (7 x))) : - \frac{9}{49} (7 x sin (7 x) + cos (7 x))

= - \frac{9}{49} (7 x sin (7 x) + cos (7 x))

解答补常数

= - \frac{9}{49} (7 x sin (7 x) + cos (7 x)) + C

作图

流行的例子

integral of 6/(4x-2)

\int \frac{6}{4 x - 2} d x

integral of 1/(usqrt(u))

\int \frac{1}{u u} d u

integral of (sin(6x))/6

\int \frac{sin ( 6 x )}{6} d x

integral of 1/(sqrt(7x^2-8))

\int \frac{1}{7 x ^{2} - 8} d x

integral of (sqrt(1+x^2))/(-5x)

\int \frac{1 + x ^{2}}{- 5 x} d x