What is the integral of 2sqrt(x)-3\sqrt[4]{x} ?

The integral of 2sqrt(x)-3\sqrt[4]{x} is 4/3 x^{3/2}-12/5 x^{5/4}+C

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integral of 2sqrt(x)-3\sqrt[4]{x}

\frac{4}{3} x^{\frac{3}{2}} - \frac{12}{5} x^{\frac{5}{4}} + C

Solution steps

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int 2 x d x = \frac{4}{3} x^{\frac{3}{2}}

= \frac{4}{3} x^{\frac{3}{2}} - \frac{12}{5} x^{\frac{5}{4}}

Add a constant to the solution

= \frac{4}{3} x^{\frac{3}{2}} - \frac{12}{5} x^{\frac{5}{4}} + C

\int \frac{1}{tanh ( 3 x )} d x

3 y^{^{''}} + 75 y = 81 sin (4 t)

y = x^{3}, (2, 8)

y^{^{''}} + 8 y^{^{'}} + 16 y = 2 e^{- 4 t}

\frac{\partial}{\partial x} (3 x ln (x y))

What is the integral of 2sqrt(x)-3\sqrt[4]{x} ?
The integral of 2sqrt(x)-3\sqrt[4]{x} is 4/3 x^{3/2}-12/5 x^{5/4}+C