What is the integral of 1/(x^{3/4)}+5.5sqrt(x) ?

The integral of 1/(x^{3/4)}+5.5sqrt(x) is 4\sqrt[4]{x}+3.66666…x^{3/2}+C

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integral of 1/(x^{3/4)}+5.5sqrt(x)

\int \frac{1}{x ^{\frac{3}{4}}} + 5.5 x d x

Solution steps

\int \frac{1}{x ^{\frac{3}{4}}} + 5.5 x 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{1}{x ^{\frac{3}{4}}} d x + \int 5.5 x d x

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

\int 5.5 x d x = 3.66666 \dots x^{\frac{3}{2}}

= 4 x^{\frac{1}{4}} + 3.66666 \dots x^{\frac{3}{2}}

Apply radical rule:

Add a constant to the solution

\int e^{c o s (t)} sin (t) d t

\frac{d}{d x} (x^{l o g_{2} (x)})

\int \frac{1}{x ^{2} \cdot x ^{2} - 4} d x

x \to 0 + lim (x^{12} ln (x))

\frac{d}{d x} (ln (x^{2} + 3 x + 3))

What is the integral of 1/(x^{3/4)}+5.5sqrt(x) ?
The integral of 1/(x^{3/4)}+5.5sqrt(x) is 4\sqrt[4]{x}+3.66666…x^{3/2}+C