What is the integral of 5x^4-3x^2+4 ?

The integral of 5x^4-3x^2+4 is x^5-x^3+4x+C

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integral of 5x^4-3x^2+4

\int 5 x^{4} - 3 x^{2} + 4 d x

x^{5} - x^{3} + 4 x + C

Solution steps

\int 5 x^{4} - 3 x^{2} + 4 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 5 x^{4} d x - \int 3 x^{2} d x + \int 4 d x

\int 5 x^{4} d x = x^{5}

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

\int 4 d x = 4 x

= x^{5} - x^{3} + 4 x

Add a constant to the solution

= x^{5} - x^{3} + 4 x + C

\int \frac{1}{( x + 1 ) x} d x

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

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

\int \frac{sec ^{2} ( w )}{1 + tan ^{2} ( w )} d w

\int (2 x^{2} y) d y

What is the integral of 5x^4-3x^2+4 ?
The integral of 5x^4-3x^2+4 is x^5-x^3+4x+C