What is the integral of (t^2sqrt(t)) ?

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

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integral of (t^2sqrt(t))

\int (t^{2} t) d t

\frac{2}{7} t^{\frac{7}{2}} + C

Solution steps

\int t^{2} t d t

Simplify

t^{2} t : t^{\frac{5}{2}}

= \int t^{\frac{5}{2}} d t

Apply the Power Rule

: \frac{2}{7} t^{\frac{7}{2}}

= \frac{2}{7} t^{\frac{7}{2}}

Add a constant to the solution

= \frac{2}{7} t^{\frac{7}{2}} + C

x = 45 - 5 y^{2}, x = 5 y^{2} - 45

\frac{d}{d x} (2 x + 3)

f (x) = (3 x)

\int \frac{x ^{2} + 3 x - 4}{x ^{3} - 4 x ^{2} + 4 x} d x

\int x^{5} cos (x^{3}) d x

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