What is the integral of 6x^2sin(x^3) ?

The integral of 6x^2sin(x^3) is -2cos(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 6x^2sin(x^3)

\int 6 x^{2} sin (x^{3}) d x

- 2 cos (x^{3}) + C

Solution steps

\int 6 x^{2} sin (x^{3}) d x

Take the constant out:

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

= 6 \cdot \int x^{2} sin (x^{3}) d x

Apply u-substitution

: \int \frac{sin ( u )}{3} d u

= 6 \cdot \int \frac{sin ( u )}{3} d u

Take the constant out:

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

= 6 \cdot \frac{1}{3} \cdot \int sin (u) d u

Use the common integral:

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

= 6 \cdot \frac{1}{3} (- cos (u))

Substitute back

u = x^{3}

= 6 \cdot \frac{1}{3} (- cos (x^{3}))

Simplify

6 \cdot \frac{1}{3} (- cos (x^{3})) : - 2 cos (x^{3})

= - 2 cos (x^{3})

Add a constant to the solution

= - 2 cos (x^{3}) + C

\int \frac{12}{x ^{2} x ^{2} + 16} d x

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

x \to 2 - lim (3)

\int \frac{z ^{2}}{1 + z ^{3}} d z

\int x^{2} x^{2} + 4 d x

What is the integral of 6x^2sin(x^3) ?
The integral of 6x^2sin(x^3) is -2cos(x^3)+C