What is the integral of x^2(x^3+1)\sqrt{x ?

The integral of x^2(x^3+1)\sqrt{x is sqrt(d)(1/4 x^4(x^3+1)-(3x^7)/(28))+C

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integral of x^2(x^3+1)\sqrt{x

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

d (\frac{1}{4} x^{4} (x^{3} + 1) - \frac{3 x ^{7}}{28}) + C

Solution steps

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

Take the constant out:

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

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

Simplify

x^{2} (x^{3} + 1) x : x^{3} (x^{3} + 1)

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

Apply Integration By Parts

: \frac{1}{4} x^{4} (x^{3} + 1) - \int \frac{3 x ^{6}}{4} d x

= d (\frac{1}{4} x^{4} (x^{3} + 1) - \int \frac{3 x ^{6}}{4} d x)

\int \frac{3 x ^{6}}{4} d x = \frac{3 x ^{7}}{28}

= d (\frac{1}{4} x^{4} (x^{3} + 1) - \frac{3 x ^{7}}{28})

Add a constant to the solution

= d (\frac{1}{4} x^{4} (x^{3} + 1) - \frac{3 x ^{7}}{28}) + C

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What is the integral of x^2(x^3+1)\sqrt{x ?
The integral of x^2(x^3+1)\sqrt{x is sqrt(d)(1/4 x^4(x^3+1)-(3x^7)/(28))+C