What is the integral of (x^3+x)^5(3x^2+1) ?

The integral of (x^3+x)^5(3x^2+1) is ((x^3+x)^6)/6+C

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integral of (x^3+x)^5(3x^2+1)

\int (x^{3} + x)^{5} (3 x^{2} + 1) d x

\frac{( x ^{3} + x ) ^{6}}{6} + C

Solution steps

\int (x^{3} + x)^{5} (3 x^{2} + 1) d x

Apply u-substitution

= \int u^{5} d u

Apply the Power Rule

= \frac{u ^{6}}{6}

Substitute back

u = x^{3} + x

= \frac{( x ^{3} + x ) ^{6}}{6}

Add a constant to the solution

= \frac{( x ^{3} + x ) ^{6}}{6} + C

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What is the integral of (x^3+x)^5(3x^2+1) ?
The integral of (x^3+x)^5(3x^2+1) is ((x^3+x)^6)/6+C