What is the integral of sin^2(x)in(x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin^2(x)in(x)

\int sin^{2} (x) d sin (x) d x

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

Solution steps

\int sin^{2} (x) d sin (x) d x

Take the constant out:

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

= d \cdot \int sin^{2} (x) sin (x) d x

Rewrite using trig identities

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

Apply u-substitution

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

= d \cdot \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

= d (- \int 1 d u + \int u^{2} d u)

\int 1 d u = u

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

= d (- u + \frac{u ^{3}}{3})

Substitute back

u = cos (x)

= d (- cos (x) + \frac{cos ^{3} ( x )}{3})

Add a constant to the solution

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

\int - 4 x e^{2 x} d x

\int sin (10 π x) d x

\int 2 x^{2} d x

\int \frac{ln ( t )}{7 t ^{3}} d t

\int 1 + 7 x d x

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