What is the integral of-8xsin(4x^2-7) ?

The integral of-8xsin(4x^2-7) is cos(4x^2-7)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-8xsin(4x^2-7)

\int - 8 x sin (4 x^{2} - 7) d x

cos (4 x^{2} - 7) + C

Solution steps

\int - 8 x sin (4 x^{2} - 7) d x

Take the constant out:

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

= - 8 \cdot \int x sin (4 x^{2} - 7) d x

Apply u-substitution

: \int \frac{sin ( 4 u - 7 )}{2} d u

= - 8 \cdot \int \frac{sin ( 4 u - 7 )}{2} d u

Take the constant out:

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

= - 8 \cdot \frac{1}{2} \cdot \int sin (4 u - 7) d u

Apply u-substitution

: \int sin (v) \frac{1}{4} d v

= - 8 \cdot \frac{1}{2} \cdot \int sin (v) \frac{1}{4} d v

Take the constant out:

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

= - 8 \cdot \frac{1}{2} \cdot \frac{1}{4} \cdot \int sin (v) d v

Use the common integral:

\int sin (v) d v = - cos (v)

= - 8 \cdot \frac{1}{2} \cdot \frac{1}{4} (- cos (v))

Substitute back

= - 8 \cdot \frac{1}{2} \cdot \frac{1}{4} (- cos (4 x^{2} - 7))

Simplify

- 8 \cdot \frac{1}{2} \cdot \frac{1}{4} (- cos (4 x^{2} - 7)) : cos (4 x^{2} - 7)

= cos (4 x^{2} - 7)

Add a constant to the solution

= cos (4 x^{2} - 7) + C

\int \frac{2 - e ^{x}}{1 + e ^{x}} d x

\int 4 (2 x - 9)^{3} d x

\int 8 x + 10 d x

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

What is the integral of-8xsin(4x^2-7) ?
The integral of-8xsin(4x^2-7) is cos(4x^2-7)+C