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

The integral of cos(x^3)x^2 is 1/3 sin(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 cos(x^3)x^2

\int cos (x^{3}) x^{2} d x

\frac{1}{3} sin (x^{3}) + C

Solution steps

\int cos (x^{3}) x^{2} d x

Apply u-substitution

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

= \int \frac{cos ( u )}{3} d u

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{3} sin (u)

Substitute back

u = x^{3}

= \frac{1}{3} sin (x^{3})

Add a constant to the solution

= \frac{1}{3} sin (x^{3}) + C

\int (8 x^{3} + 5) d x

\int \frac{sec ^{2} ( z )}{z} d z

\int (\frac{1}{sin ^{2} ( x )} + 1) d (sin (x)) d x

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

\int 7 \frac{( ln ( z ) ) ^{2}}{z} d z

What is the integral of cos(x^3)x^2 ?
The integral of cos(x^3)x^2 is 1/3 sin(x^3)+C