What is the integral of (x^3+x^{-4}+x^{3/4}) ?

The integral of (x^3+x^{-4}+x^{3/4}) is (x^4)/4-1/(3x^3)+4/7 x^{7/4}+C

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integral of (x^3+x^{-4}+x^{3/4})

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

\frac{x ^{4}}{4} - \frac{1}{3 x ^{3}} + \frac{4}{7} x^{\frac{7}{4}} + C

Solution steps

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

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

\int x^{- 4} d x = - \frac{1}{3 x ^{3}}

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

= \frac{x ^{4}}{4} - \frac{1}{3 x ^{3}} + \frac{4}{7} x^{\frac{7}{4}}

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{1}{3 x ^{3}} + \frac{4}{7} x^{\frac{7}{4}} + C

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

\frac{1}{z ^{2} + 1}

x^{- 5} (1 + x^{- 1}), at x = 1

y = x^{2}, y^{2} = x

f (x) = 5 x - x^{2}

What is the integral of (x^3+x^{-4}+x^{3/4}) ?
The integral of (x^3+x^{-4}+x^{3/4}) is (x^4)/4-1/(3x^3)+4/7 x^{7/4}+C