What is the integral of (x/7-3/4 x^4) ?

The integral of (x/7-3/4 x^4) is (x^2)/(14)-(3x^5)/(20)+C

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integral of (x/7-3/4 x^4)

\int (\frac{x}{7} - \frac{3}{4} x^{4}) d x

\frac{x ^{2}}{14} - \frac{3 x ^{5}}{20} + C

Solution steps

\int \frac{x}{7} - \frac{3}{4} x^{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 \frac{x}{7} d x - \int \frac{3}{4} x^{4} d x

\int \frac{x}{7} d x = \frac{x ^{2}}{14}

\int \frac{3}{4} x^{4} d x = \frac{3 x ^{5}}{20}

= \frac{x ^{2}}{14} - \frac{3 x ^{5}}{20}

Add a constant to the solution

= \frac{x ^{2}}{14} - \frac{3 x ^{5}}{20} + C

2 t^{2} y^{^{''}} + 3 t y^{^{'}} - y = 0

\int_{0}^{\infty} e^{- \frac{x}{2}} d x

\int_{0}^{3} (3 x - x^{2}) d x

3 e^{- 2 t} cos (3 t)

x \to 3 lim (\frac{1}{3 - x})

What is the integral of (x/7-3/4 x^4) ?
The integral of (x/7-3/4 x^4) is (x^2)/(14)-(3x^5)/(20)+C