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

The integral of (3x^2-sqrt(5x+2)) is x^3-2/15 (5x+2)^{3/2}+C

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integral of (3x^2-sqrt(5x+2))

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

x^{3} - \frac{2}{15} (5 x + 2)^{\frac{3}{2}} + C

Solution steps

\int 3 x^{2} - 5 x + 2 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 3 x^{2} d x - \int 5 x + 2 d x

\int 3 x^{2} d x = x^{3}

\int 5 x + 2 d x = \frac{2}{15} (5 x + 2)^{\frac{3}{2}}

= x^{3} - \frac{2}{15} (5 x + 2)^{\frac{3}{2}}

Add a constant to the solution

= x^{3} - \frac{2}{15} (5 x + 2)^{\frac{3}{2}} + C

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

\int x (x^{2} + 5)^{9} d x

\int \frac{cos ( x )}{sin ^{2} ( x ) + sin ( x ) - 2} d x

\int \frac{cos ^{3} ( 5 x )}{sin ^{4} ( 5 x )} d x

What is the integral of (3x^2-sqrt(5x+2)) ?
The integral of (3x^2-sqrt(5x+2)) is x^3-2/15 (5x+2)^{3/2}+C