Liesehf

2021-11-17

Evaluate the indefinite integral.

$\int {(2{x}^{3}-7)}^{2}dx$

Tamara Donohue

Beginner2021-11-18Added 11 answers

Step 1

We have to evaluate$\int {(2{x}^{3}-7)}^{2}dx$

We know that$(a-b)}^{2}={a}^{2}-2ab+{b}^{2$

And$\int {x}^{n}dx=\frac{{x}^{n+1}}{n+1}+c$

Integrating the given integral using the above formula,

$\int {(2{x}^{3}-7)}^{2}dx=\int [{\left(2{x}^{3}\right)}^{2}-2\cdot 2{x}^{3}\cdot 7+{\left(7\right)}^{2}]dx$

$=\int [4{x}^{6}-28{x}^{3}+49]dx$

$=\int 4{x}^{6}dx-\int 28{x}^{3}+\int 49dx$

$=4\cdot \frac{{x}^{6+1}}{6+1}-28\cdot \frac{{x}^{3+1}}{3+1}+49x+C$ , where C is integration constant.

$=\frac{4}{7}{x}^{7}-7{x}^{4}+49x+C$

Step 2

Hence, required integral is$\frac{4}{7}{x}^{7}-7{x}^{4}+49x+C$ .

We have to evaluate

We know that

And

Integrating the given integral using the above formula,

Step 2

Hence, required integral is

Nicole Keller

Beginner2021-11-19Added 14 answers

Step 1: Expand.

$\int 4{x}^{6}-28{x}^{3}+49dx$

Step 2: Use Power Rule:$\int {x}^{n}dx=\frac{{x}^{n+1}}{n+1}+C$ .

$\frac{4{x}^{7}}{7}-7{x}^{4}+49x$

Step 3: Add constant.

$\frac{4{x}^{7}}{7}-7{x}^{4}+49x+C$

Step 2: Use Power Rule:

Step 3: Add constant.

What is the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1)?

How to expand and simplify $2(3x+4)-3(4x-5)$?

Find an equation equivalent to ${x}^{2}-{y}^{2}=4$ in polar coordinates.

How to graph $r=5\mathrm{sin}\theta$?

How to find the length of a curve in calculus?

When two straight lines are parallel their slopes are equal.

A)True;

B)FalseIntegration of 1/sinx-sin2x dx

Converting percentage into a decimal. $8.5\%$

Arrange the following in the correct order of increasing density.

Air

Oil

Water

BrickWhat is the exact length of the spiraling polar curve $r=5{e}^{2\theta}$ from 0 to $2\pi$?

What is $\frac{\sqrt{7}}{\sqrt{11}}$ in simplest radical form?

What is the slope of the tangent line of $r=-2\mathrm{sin}\left(3\theta \right)-12\mathrm{cos}\left(\frac{\theta}{2}\right)$ at $\theta =\frac{-\pi}{3}$?

How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

Use the summation formulas to rewrite the expression $\Sigma \frac{2i+1}{{n}^{2}}$ as i=1 to n without the summation notation and then use the result to find the sum for n=10, 100, 1000, and 10000.

How to calculate the right hand and left hand riemann sum using 4 sub intervals of f(x)= 3x on the interval [1,5]?