What is the integral of sin(x)*cos^3(x) ?

The integral of sin(x)*cos^3(x) is -(cos^4(x))/4+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(x)*cos^3(x)

\int sin (x) \cdot cos^{3} (x) d x

- \frac{cos ^{4} ( x )}{4} + C

Solution steps

\int sin (x) cos^{3} (x) d x

Apply u-substitution

: \int - u^{3} d u

= \int - u^{3} d u

Take the constant out:

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

= - \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= - \frac{u ^{4}}{4}

Substitute back

u = cos (x)

= - \frac{cos ^{4} ( x )}{4}

Add a constant to the solution

= - \frac{cos ^{4} ( x )}{4} + C

f (x) = 8 x sin (x)

x \to 0 lim (ln (x) \cdot ln (1 - x))

\int (x^{2} - 8)^{4} (2 x) d x

\frac{\partial}{\partial x} (\frac{6 x - 7 y}{6 x + 7 y})

y = 2 (1.1)^{t}

What is the integral of sin(x)*cos^3(x) ?
The integral of sin(x)*cos^3(x) is -(cos^4(x))/4+C