What is the integral of x^3sin(1/3)x ?

The integral of x^3sin(1/3)x is 1/5 sin(1/3)x^5+C

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integral of x^3sin(1/3)x

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

\frac{1}{5} sin (\frac{1}{3}) x^{5} + C

Solution steps

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

Take the constant out:

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

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

Simplify

x^{3} x : x^{4}

= sin (\frac{1}{3}) \cdot \int x^{4} d x

Apply the Power Rule

: \frac{x ^{5}}{5}

= sin (\frac{1}{3}) \frac{x ^{5}}{5}

Simplify

sin (\frac{1}{3}) \frac{x ^{5}}{5} : \frac{1}{5} sin (\frac{1}{3}) x^{5}

= \frac{1}{5} sin (\frac{1}{3}) x^{5}

Add a constant to the solution

= \frac{1}{5} sin (\frac{1}{3}) x^{5} + C

\int \frac{5}{e ^{- x}} d x

\int \frac{1}{a + b x} d x

\int \frac{3 x}{x ^{3}} d x

\int y^{- \frac{1}{2}} (y^{4} + 2 y^{2} - 1) d y

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

What is the integral of x^3sin(1/3)x ?
The integral of x^3sin(1/3)x is 1/5 sin(1/3)x^5+C