What is the integral of xsin(5)x^2 ?

The integral of xsin(5)x^2 is 1/4 sin(5)x^4+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of xsin(5)x^2

\int x sin (5) x^{2} d x

\frac{1}{4} sin (5) x^{4} + C

Solution steps

\int x sin (5) x^{2} d x

Take the constant out:

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

= sin (5) \cdot \int x x^{2} d x

Simplify

x x^{2} : x^{3}

= sin (5) \cdot \int x^{3} d x

Apply the Power Rule

: \frac{x ^{4}}{4}

= sin (5) \frac{x ^{4}}{4}

Simplify

sin (5) \frac{x ^{4}}{4} : \frac{1}{4} sin (5) x^{4}

= \frac{1}{4} sin (5) x^{4}

Add a constant to the solution

= \frac{1}{4} sin (5) x^{4} + C

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

\int (ln (x) + x ln (x)) d x

\int \frac{1}{3 x ( x ^{2} + 1 ) ^{2}} d x

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

\int 18 (3 x + 4)^{5} d x

What is the integral of xsin(5)x^2 ?
The integral of xsin(5)x^2 is 1/4 sin(5)x^4+C