What is the integral of 2x^3+5x^2-2x+pi ?

The integral of 2x^3+5x^2-2x+pi is (x^4)/2+(5x^3)/3-x^2+pix+C

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integral of 2x^3+5x^2-2x+pi

\int 2 x^{3} + 5 x^{2} - 2 x + π d x

\frac{x ^{4}}{2} + \frac{5 x ^{3}}{3} - x^{2} + π x + C

Solution steps

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

\int 2 x^{3} d x = \frac{x ^{4}}{2}

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

\int π d x = π x

= \frac{x ^{4}}{2} + \frac{5 x ^{3}}{3} - x^{2} + π x

Add a constant to the solution

= \frac{x ^{4}}{2} + \frac{5 x ^{3}}{3} - x^{2} + π x + C

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

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

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

\int \frac{1}{2 sin ( x ) + cos ( x ) + 5} d x

\int \frac{1}{y ^{2} + 3 y + 1} d y

What is the integral of 2x^3+5x^2-2x+pi ?
The integral of 2x^3+5x^2-2x+pi is (x^4)/2+(5x^3)/3-x^2+pix+C