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

The integral of (4x^{3/4}+4) is 16/7 x^{7/4}+4x+C

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

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

\frac{16}{7} x^{\frac{7}{4}} + 4 x + C

Solution steps

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

\int 4 x^{\frac{3}{4}} d x = \frac{16}{7} x^{\frac{7}{4}}

\int 4 d x = 4 x

= \frac{16}{7} x^{\frac{7}{4}} + 4 x

Add a constant to the solution

= \frac{16}{7} x^{\frac{7}{4}} + 4 x + C

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What is the integral of (4x^{3/4}+4) ?
The integral of (4x^{3/4}+4) is 16/7 x^{7/4}+4x+C