Ace Your JEE Main Integration Skills 2026 – Conquer Calculus with Confidence!

To find the integral of arcsin(x) with respect to x, we can use integration by parts. The formula for integration by parts is:

\[

\int u \, dv = uv - \int v \, du

\]

For our case, we can let:

- \( u = \arcsin(x) \) (which gives \( du = \frac{1}{\sqrt{1-x^2}} \, dx \))

- \( dv = dx \) (which gives \( v = x \))

Applying integration by parts gives us:

\[

\int \arcsin(x) \, dx = x \arcsin(x) - \int x \cdot \frac{1}{\sqrt{1-x^2}} \, dx

\]

Now we need to evaluate the integral \( \int \frac{x}{\sqrt{1-x^2}} \, dx \). This can be solved by recognizing that:

\[

\int \frac{x}{\sqrt{1-x^2}} \, dx = -\sqrt{1-x^2}

\]

Thus, we can substitute back into our expression:

\[

\int \arcsin(x) \