What is the integral of (sqrt(t^4+7t))(4t^3+7) ?

The integral of (sqrt(t^4+7t))(4t^3+7) is 2/3 (t^4+7t)^{3/2}+C

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integral of (sqrt(t^4+7t))(4t^3+7)

\int (t^{4} + 7 t) (4 t^{3} + 7) d t

\frac{2}{3} (t^{4} + 7 t)^{\frac{3}{2}} + C

Solution steps

\int t^{4} + 7 t (4 t^{3} + 7) d t

Apply u-substitution

= \int u d u

Apply the Power Rule

= \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = t^{4} + 7 t

= \frac{2}{3} (t^{4} + 7 t)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (t^{4} + 7 t)^{\frac{3}{2}} + C

What is the integral of (sqrt(t^4+7t))(4t^3+7) ?
The integral of (sqrt(t^4+7t))(4t^3+7) is 2/3 (t^4+7t)^{3/2}+C