Finding an Indefinite Integral In Exercises $7-10,$ find the indefinite integral and check the result by differentiation.

$7.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(x^{3}4)dx$

$8.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(4x^{2}x3)dx$

$9.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{6}{\sqrt[3]{x}}dx$

$10.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(2cs{c}^{2}x-9sinx)dx$

Finding a Particular Solution In Exercises $11$ and $12,$ find the particular solution of the differential equation that satisfies the initial condition$($s$).$

$11.f^{\text{'}}(x)=-6x,f(1)=-2$

$12.f^{\text{'}\text{'}}(x)=24x,f^{\text{'}}(-1)=7,f(1)=-4$