Evaluate the integrals. Check your results by differentiation.

$$\int\left(3 x^3+1\right)^4 9 x^2 d x$$

Evaluate the integrals. Check your results by differentiation.

$$\int 5 x^3\left(3 x^4+7\right)^{-4} d x$$

Use implicit differentiation to find dy/dx and then $d^{2} y / d x^{2}.$ Write the solutions in terms of x and y only. $x^{2 / 3}+y^{2 / 3}=1$

Find the indicated integral. Check your answers by differentiation.

$$\int\left(\sqrt{x^3}-\frac{1}{2 \sqrt{x}}+\sqrt{2}\right) d x$$

Find an antiderivative for the given function. If you can, try to do mentally. Check your answers by differentiation.

$$x^{-4}+2 x+3$$

Find the integral in Problem. Check your answer by differentiation.

$$\int t \cos \left(t^2\right) d t$$

Find the indefinite integral, and check your answer by differentiation.

$$\int\left(e^t+t^e\right) d t$$

Find the indefinite integral and check the result by differentiation.

$$\displaystyle \int (8x^{3}-9x^{2}+4)dx$$

Find the indicated integral. Check your answers by differentiation.

$$\int\left(3 t^2-\sqrt{5 t}+2\right) d t$$

Find the indicated integral. Check your answers by differentiation.

$$\int e^{-0.02 t}\left(e^{-0.13 t}+4\right) d t$$

Use implicit differentiation to find $y^{\prime}$ and evaluate $y^{\prime}$ at the indicated point. $y-5 x^{2}+3=0 ;(1,2)$

Determine the following indefinite integrals. Check your work by differentiation. $\int \frac{12 t^{8}-t}{t^{3 / 2}} d t$

Find the indicated integral. Check your answer by differentiation. $\int\left(3 t^{2}-\sqrt{5 t}+2\right) d t$

Use Logarithmic differentiation to find $y^{\prime}$ Assume that variable is restricted so that all arguments of logarithm functions are positive

$$y=x^{\cos x}$$