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

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

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integral of xsin(4)x^2

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

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

Solution steps

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

Take the constant out:

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

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

Simplify

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

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

\int sec^{3} (7 x) tan^{5} (7 x) d x

f (t) = t^{2} - 2 t

y^{^{''''}} + 32 y^{^{''}} + 256 y = 0

\int \frac{x ^{2} - 17 x + 4}{x + 7} d x

\frac{d}{d x} (x^{2} + 4 x - 8)

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