What is the integral of (3x-4/3 x^{3/2}) ?

The integral of (3x-4/3 x^{3/2}) is (3x^2)/2-8/15 x^{5/2}+C

Popular >

integral of (3x-4/3 x^{3/2})

\int (3 x - \frac{4}{3} x^{\frac{3}{2}}) d x

\frac{3 x ^{2}}{2} - \frac{8}{15} x^{\frac{5}{2}} + C

Solution steps

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

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

\int \frac{4}{3} x^{\frac{3}{2}} d x = \frac{8}{15} x^{\frac{5}{2}}

= \frac{3 x ^{2}}{2} - \frac{8}{15} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{3 x ^{2}}{2} - \frac{8}{15} x^{\frac{5}{2}} + C

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

t^{3} - 15 t^{2} + 72 t

\frac{d}{d x} (e^{- a x} cos (b x))

y = ∣ x ∣, y = x^{2}

\int \frac{sin ( θ ) - 1}{cos ^{2} ( θ )} d θ

What is the integral of (3x-4/3 x^{3/2}) ?
The integral of (3x-4/3 x^{3/2}) is (3x^2)/2-8/15 x^{5/2}+C