calculus · worked example

Solve ∫ cos(x) dx = sin(x) + C

Method: 標準積分. Verified step-by-step solution with our free AI math solver.
Problem

cos(x)dx\int \cos(x) \, dx

Step-by-step solution

  1. 回想:ddxsinx=cosx\frac{d}{dx}\sin x = \cos x

  2. 因此 sinx\sin xcosx\cos x 的一個反導數(原函數)。

  3. 因此 cosxdx=sinx+C\int \cos x \, dx = \sin x + C

  4. 注意:cos\cos 的積分是 +sin+\sin(正號);與 sin\sin 的積分相對照,後者是 cos-\cos(負號),符號相反。

Answer

sin(x)+C\sin(x) + C

Want to solve a different problem? Open the integral solver →