Simplify $\left(\sqrt{1+x}\right)^4$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $\frac{1}{2}$ and $n$ equals $4$
We can solve the integral $\int\frac{3}{1+x}dx$ by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it $u$), which when substituted makes the integral easier. We see that $1+x$ it's a good candidate for substitution. Let's define a variable $u$ and assign it to the choosen part
$u=1+x$
Intermediate steps
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Now, in order to rewrite $dx$ in terms of $du$, we need to find the derivative of $u$. We need to calculate $du$, we can do that by deriving the equation above
$du=dx$
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Substituting $u$ and $dx$ in the integral and simplify
Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more
In mathematics, an equation is a statement of an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions.