What is the integral of (1-sin^2(x))cos(x) ?

The integral of (1-sin^2(x))cos(x) is sin(x)-(sin^3(x))/3+C

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integral of (1-sin^2(x))cos(x)

\int (1 - sin^{2} (x)) cos (x) d x

sin (x) - \frac{sin ^{3} ( x )}{3} + C

Solution steps

\int (1 - sin^{2} (x)) cos (x) d x

Apply u-substitution

: \int 1 - u^{2} d u

= \int 1 - u^{2} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d u - \int u^{2} d u

\int 1 d u = u

\int u^{2} d u = \frac{u ^{3}}{3}

= u - \frac{u ^{3}}{3}

Substitute back

u = sin (x)

= sin (x) - \frac{sin ^{3} ( x )}{3}

Add a constant to the solution

= sin (x) - \frac{sin ^{3} ( x )}{3} + C

\frac{d}{d x} (\frac{x ^{5} - 5}{x + 1})

\frac{\partial}{\partial x} (2 x^{2} y + sin (x^{4}))

x \to 1 lim (x^{\frac{8}{1 - x}})

\frac{\partial}{\partial x} ((x^{3} + y^{3})^{\frac{1}{3}})

\int \frac{1}{x 9 - 4 x ^{2}} d x

What is the integral of (1-sin^2(x))cos(x) ?
The integral of (1-sin^2(x))cos(x) is sin(x)-(sin^3(x))/3+C