What is the integral of xsin^2(x ?

The integral of xsin^2(x is (x^3sin^2(d))/3+C

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integral of xsin^2(x

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

\frac{x ^{3} sin ^{2} ( d )}{3} + C

Solution steps

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

Take the constant out:

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

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

Simplify

xx : x^{2}

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

Apply the Power Rule

: \frac{x ^{3}}{3}

= sin^{2} (d) \frac{x ^{3}}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x ^{3} sin ^{2} ( d )}{3}

Add a constant to the solution

= \frac{x ^{3} sin ^{2} ( d )}{3} + C

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

\int 88 x^{- \frac{1}{5}} tan (x^{\frac{4}{5}}) d x

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

\int \frac{sin ( x ) + cos ( x )}{sin ( x )} d x

\int \frac{x}{3 x ^{2} + 3} d x

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