Chapter 12

The Integral

Educators


Problem 1

Now evaluate the following integrals.
$\int \frac{1}{x^{4}} d x$

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Problem 2

Now evaluate the following integrals.
$\int \frac{5}{\sqrt{x}} d x$

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Problem 3

Now evaluate the following integrals.
$\int\left(5 x^{4}-3 x^{2}+2 x+6\right) d x$

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Problem 4

Now evaluate the following integrals.
$\int\left(3 x^{-3}-2 x^{-2}+x^{4}+16 x^{7}\right) d x$

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Problem 5

Now evaluate the following integrals.
$\int x^{\frac{1}{3}}(2+x) d x$

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Problem 6

Now evaluate the following integrals.
$\int\left(x^{3}+x\right)^{2} d x$

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Problem 7

Now evaluate the following integrals.
$\int \frac{x^{6}-2 x^{4}+1}{x^{2}} d x$

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Problem 8

Now evaluate the following integrals.
$\int x(x-1)^{3} d x$

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Problem 9

Now evaluate the following integrals.
$\int \sec x(\sec x+\tan x) d x$

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Problem 10

Now evaluate the following integrals.
$\int\left(\sec ^{2} x+x\right) d x$

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Problem 11

Now evaluate the following integrals.
$\int \frac{\cos ^{3} x+4}{\cos ^{2} x} d x$

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Problem 12

Now evaluate the following integrals.
$\int \frac{\sin 2 x}{\cos x} d x$

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Problem 13

Now evaluate the following integrals.
$\int\left(1+\cos ^{2} x \sec x\right) d x$

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Problem 14

Now evaluate the following integrals.
$\int \frac{1}{\csc x} d x$

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Problem 15

Now evaluate the following integrals.
$\int\left(x-\frac{2}{\cos ^{2} x}\right) d x$

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