Calculate the integral and write the answer in simplest form. int(-2x^(2)+5)dx Answer:

Given Integral: We are given the integral to solve: ∫(-2x^2 + 5)dx We will integrate the function term by term.Integrating -2x^2: First, we integrate the term -2x^2 with respect to x. The integral of x^n with respect to x is (x^(n+1))/(n+1), so the integral of -2x^2 is: ∫(-2x^2)dx = -2 * ∫(x^2)dx = -2 * (x^(2+1))/(2+1) = -2 * (x^3)/3Integrating 5: Next, we integrate the constant term 5 with respect to x. The integral of a constant a with respect to x is ax, so the integral of 5 is: ∫(5)dx = 5xCombining Integrals: Now, we combine the results of the two integrals and add the constant of integration C. The combined integral is: -2 * (x^3)/3 + 5x + CFinal Answer: We simplify the expression by combining like terms, if any. However, in this case, there are no like terms to combine, so the expression is already in its simplest form. The final answer is: -2/3 * x^3 + 5x + C

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Calculate the integral and write the answer in simplest form.

int(-2x^(2)+5)dx
Answer:

Calculate the integral and write the answer in simplest form. $\newline$ $\int\left(-2 x^{2}+5\right) d x$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Calculus

Find indefinite integrals using the substitution

Full solution

Q. Calculate the integral and write the answer in simplest form.

\newline

\int\left(-2 x^{2}+5\right) d x

\newline

Answer:

Given Integral: We are given the integral to solve: $\newline$ $\int(-2x^2 + 5)\,dx$ $\newline$ We will integrate the function term by term.
Integrating $-2x^2$ : First, we integrate the term $-2x^2$ with respect to $x$ . The integral of $x^n$ with respect to $x$ is $\frac{x^{(n+1)}}{n+1}$ , so the integral of $-2x^2$ is: $\int(-2x^2)dx = -2 \times \int(x^2)dx = -2 \times \frac{x^{(2+1)}}{2+1} = -2 \times \frac{x^3}{3}$
Integrating $5$ : Next, we integrate the constant term $5$ with respect to $x$ . The integral of a constant $a$ with respect to $x$ is $ax$ , so the integral of $5$ is: $\int(5)dx = 5x$
Combining Integrals: Now, we combine the results of the two integrals and add the constant of integration $C$ . The combined integral is: $-2 \times \frac{x^3}{3} + 5x + C$
Final Answer: We simplify the expression by combining like terms, if any. However, in this case, there are no like terms to combine, so the expression is already in its simplest form. $\newline$ The final answer is: $\newline$ $-\frac{2}{3} \times x^3 + 5x + C$