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Hint: Integral expression contains a function and its derivative, hence we use substitution method to reduce the integral into standard form.
Consider the expression,
It consists of two functions, where one function i.e. is the derivative of another which is .
So, we can use the method of integration by substitution.
In this method we substitute one of the functions to reduce the expression into standard form.
Now let us consider,
Differentiating both sides with respect to x, we get
We know,
Now,
Substitute in the expression, we get
We know,
So, after integrating we get
Re-substitute the value of t in terms of x, we get
Note: Whenever an integrating expression consists of more than one function convert it into standard form by reduction method of integration such as substitution method of integration
Consider the expression,
It consists of two functions, where one function i.e. is the derivative of another which is .
So, we can use the method of integration by substitution.
In this method we substitute one of the functions to reduce the expression into standard form.
Now let us consider,
Differentiating both sides with respect to x, we get
We know,
Now,
Substitute in the expression, we get
We know,
So, after integrating we get
Re-substitute the value of t in terms of x, we get
Note: Whenever an integrating expression consists of more than one function convert it into standard form by reduction method of integration such as substitution method of integration
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