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APEX Calculus

Exercises 5.6 Review Exercises

Exercise Group.

Evaluate the given indefinite integral.

1.

\(\int \left({x^{3}+7x^{2}+9x-4}\right)\, dx\)

2.

\(\int \left({\csc\mathopen{}\left(x\right)\cot\mathopen{}\left(x\right)+\sec\mathopen{}\left(x\right)\tan\mathopen{}\left(x\right)-\csc^{2}\mathopen{}\left(x\right)}\right)\, dx\)

3.

\(\int \left({\sqrt[3]{t}+\frac{1}{t^{3}}+3^{t}}\right)\, dt\)

4.

\(\int \left({\frac{1}{x}+\sec\mathopen{}\left(x\right)\tan\mathopen{}\left(x\right)}\right)\, dx\)

Exercise Group.

Find the general antiderivative of the given function.

5.

\(f(x) = {6\sec\mathopen{}\left(x\right)\tan\mathopen{}\left(x\right)}\)

6.

\(f(x) = {\frac{5}{x}}\)

7.

\(g(t) = {t+7t^{4}+6t^{5}}\)

8.

\(g(t) = {5\cdot 6^{t}}\)

9.

\(g(t) = \cos(t) + \sin(t)\)

10.

\(f(x) = \frac{1}{\sqrt{x}}\)