Tutor profile: Robby G.

Evaluate the indefinite integral: $$\int{(2x-5)^{10}}dx$$

Utilize the method of u-substitution: Let $$u=2x-5$$. Then $$du=2$$. Rewrite the original integral using these values: $$\int{\frac{1}{2}u^{10}du}$$. Integrate as you normally would: $$\frac{1}{22}u^{11}+C$$. Substitute the value of u back in: $$\frac{1}{22}(2x-5)^{11}+C$$

___ are many species of insects across the world that make ___ presence known through a bite or sting. A. They're, their B. There, they're C. There, their D. They're, they're E. None of the above

C. There, their

Solve the following differential equation: $$\frac{dy}{dt}=3y-1$$

Using the ODE shortcut, "divide" on both sides producing: $$\frac{dy}{3y-1}=dt$$. Then, integrate both sides: $$\int{\frac{dy}{3y-1}}=\int{dt}$$. We get: $$\frac{1}{3}\ln{|3y-1|}=t+C$$ Solve for y: $$\ln{|3y-1|}=3t+C$$ Cont: $$|3y-1|=Ce^{3t}$$ Cont: $$y=Ce^{3t}+\frac{1}{3}$$