Solving the Integral of Cos(x) with Respect to x | Integration by Substitution Method

∫(cosx)dx

To solve the integral of cos(x) with respect to x, we can use integration by substitution

To solve the integral of cos(x) with respect to x, we can use integration by substitution.

Let’s assign a new variable, u, and set it equal to sin(x). Therefore, du/dx = cos(x), and we can rewrite the integral as:

∫(cos(x))dx = ∫(1)cos(x)dx = ∫(1)du

Now, integrating 1 with respect to u is straightforward. It becomes:

∫(1)du = u + C

Substituting back u = sin(x), we have:

∫(cos(x))dx = sin(x) + C

Therefore, the antiderivative of cos(x) with respect to x is sin(x) + C, where C is the constant of integration.

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