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

The integral of (sin(2)x^2)^2xcos(2)x^2 is (sin^2(2))/8 cos(2)x^8+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^2)^2xcos(2)x^2

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

\frac{sin ^{2} ( 2 )}{8} cos (2) x^{8} + C

Solution steps

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

Take the constant out:

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

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

Simplify

(sin (2) x^{2})^{2} x x^{2} : sin^{2} (2) x^{7}

= cos (2) \cdot \int sin^{2} (2) x^{7} d x

Take the constant out:

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

= cos (2) sin^{2} (2) \cdot \int x^{7} d x

Apply the Power Rule

: \frac{x ^{8}}{8}

= cos (2) sin^{2} (2) \frac{x ^{8}}{8}

Simplify

cos (2) sin^{2} (2) \frac{x ^{8}}{8} : \frac{sin ^{2} ( 2 )}{8} cos (2) x^{8}

= \frac{sin ^{2} ( 2 )}{8} cos (2) x^{8}

Add a constant to the solution

= \frac{sin ^{2} ( 2 )}{8} cos (2) x^{8} + C

\frac{d y}{d x} + y^{3} x + 3 y = 0

(t e^{t})^{^{'}}

\int 5 x^{3} (ln (x) - 2) d x

x \to \infty lim (\frac{30}{1 + x ^{10}})

\int \frac{cos ( 2 x ) - 1}{cos ( 2 x ) + 1} d x

What is the integral of (sin(2)x^2)^2xcos(2)x^2 ?
The integral of (sin(2)x^2)^2xcos(2)x^2 is (sin^2(2))/8 cos(2)x^8+C