Is this correct Computation of derivative and indefinite integral?
I just typed this "xsin(x+1)e^x" into input field for testing. Find below what I got output from CalcMentor.
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**Problem:** xsin(x+1)e^x
**Answer:** $$x e^{x} \sin{\left(x + 1 \right)}$$
**Step 1: Identify the Components**
The given expression $x\sin(x+1)e^{x}$ consists of three main components: a variable $x$, a trigonometric function $\sin(x+1)$, and an exponential function $e^{x}$.
**Step 2: Apply the Distributive Property and Simplify**
Since there are no like terms or obvious simplifications within the expression, and given that multiplication is associative, we can consider the expression as already simplified in terms of the operations involved. The expression is a product of $x$, $\sin(x+1)$, and $e^{x}$.
**Step 3: Recognize the Final Form**
Given the nature of the components, the expression $x\sin(x+1)e^{x}$ is already in a simplified form because there are no common factors to factor out, no like terms to combine, and no further simplification can be achieved through algebraic or trigonometric identities without specific instructions or context for simplification.
Therefore, the answer is:
$$x e^{x} \sin{\left(x + 1 \right)}$$
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*Solved by [CalcMentor AI](https://derivativecalculus.com/calcmentor.html) — Free · No Sign-up*
""
""
**Problem:** xsin(x+1)e^x
**Answer:** $$x e^{x} \sin{\left(x + 1 \right)}$$
**Step 1: Identify the Components**
The given expression $x\sin(x+1)e^{x}$ consists of three main components: a variable $x$, a trigonometric function $\sin(x+1)$, and an exponential function $e^{x}$.
**Step 2: Apply the Distributive Property and Simplify**
Since there are no like terms or obvious simplifications within the expression, and given that multiplication is associative, we can consider the expression as already simplified in terms of the operations involved. The expression is a product of $x$, $\sin(x+1)$, and $e^{x}$.
**Step 3: Recognize the Final Form**
Given the nature of the components, the expression $x\sin(x+1)e^{x}$ is already in a simplified form because there are no common factors to factor out, no like terms to combine, and no further simplification can be achieved through algebraic or trigonometric identities without specific instructions or context for simplification.
Therefore, the answer is:
$$x e^{x} \sin{\left(x + 1 \right)}$$
---
*Solved by [CalcMentor AI](https://derivativecalculus.com/calcmentor.html) — Free · No Sign-up*
""