Question

integration of 4^3×3√x​

Answer 1

$\large\rm { f(x) = 4^{3} \times \sqrt[3]{x}}$

$\large\rm { F(x) = \displaystyle\int \rm{ f(x) \ dx}}$

$\large\rm { \displaystyle\int \rm{ \frac{4}{3} \times \sqrt[3]{x} \ dx}}$

since 4/3 is constant, w.r.t.x, move it out from integral.

$\large\rm { = \frac{4}{3} \int \sqrt[3]{x} \ dx}$

$\large\rm { = \frac{4}{3} \int x^{\frac{1}{3}} \ dx}$

$\large\rm { = \frac{4}{3} \bigg ( \frac{3}{4} x^{\frac{4}{3}} + C \bigg ) }$

$\large\rm { = x^{\frac{4}{3}} + C}$