What is the integral of (xIn^5(x^2+3))/(x^2+3) ?

The integral of (xIn^5(x^2+3))/(x^2+3) is (In^5x^2)/2+C

Popular >

integral of (xIn^5(x^2+3))/(x^2+3)

\int \frac{x I n ^{5} ( x ^{2} + 3 )}{x ^{2} + 3} d x

\frac{I n ^{5} x ^{2}}{2} + C

Solution steps

\int \frac{x I n ^{5} ( x ^{2} + 3 )}{x ^{2} + 3} d x

Take the constant out:

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

= I n^{5} \cdot \int \frac{( 3 + x ^{2} ) x}{3 + x ^{2}} d x

Cancel the common factor:

3 + x^{2}

= I n^{5} \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= I n^{5} \frac{x ^{2}}{2}

Multiply fractions:

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

= \frac{I n ^{5} x ^{2}}{2}

Add a constant to the solution

= \frac{I n ^{5} x ^{2}}{2} + C

\int \frac{9 x ^{2} - 2 x}{1 - x ^{2} + 3 x ^{3}} d x

\int (10 x + 2) d x

\int cos (\frac{2 x}{5}) d x

\int 18 - 8 x + x^{2} d x

\int \frac{1}{51 - 70 x - 25 x ^{2}} d x

What is the integral of (xIn^5(x^2+3))/(x^2+3) ?
The integral of (xIn^5(x^2+3))/(x^2+3) is (In^5x^2)/2+C