What is the antiderivative of $sinx^3$ ?

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Answer 1 · 2017-06-13T16:21:03

If you mean $(sinx)^3$ , please see below. If you mean $sin(x^3)$ , I can't help.

Here is one possibility

$int (sinx)^3 dx = int sin^2x sinx dx$

$= int ((1-cos^2 x) sinx dx$

$= int sinx dx + int underbrace(cos^2x)_u underbrace((-sinx) dx)_(du)$

$= -cosx + cos^3x/3 +C$

As is typical of expressions involving trigonometric functions, there are other ways to express this family of functions.

(WolframAlpha gives $1/12(cos(3x)-9cosx)+C$ and simplifies the difference between our basic answers to $0$ .)

What is the antiderivative of sinx^3sinx^3?