import streamlit as st
from sympy import (
    symbols, integrate, diff, exp, log, ln, sin, cos, tan, sec, csc, cot, latex, SympifyError, sympify
)

# Define the Streamlit app
def main():
    st.set_page_config(layout="wide", page_title="Integration by Parts Solver")
    
    st.title("Integration by Parts - Step-by-Step Solver")
    st.markdown(
        """
        ## Formula for Integration by Parts
\[
        \\int u \\cdot v' \\, dx = u \\cdot v - \\int v \\cdot u' \\, dx
\]
        """
    )

    # Sidebar for input
    st.sidebar.header("Input Section")
    st.sidebar.markdown("Provide the integrand and u for integration by parts.")
    
    # Sidebar inputs
    function_input = st.sidebar.text_input(
        "Enter the integrand (e.g., x * exp(x), cos(ln(x)), x^2 * sin(x)):",
        "x * exp(x)"
    )
    u_input = st.sidebar.text_input(
        "Choose 'u' (e.g., x for x * exp(x) or ln(x)):", "x"
    )
    solve_button = st.sidebar.button("Solve")

    if solve_button:
        try:
            # Define the variable and import common functions for eval()
            x = symbols("x")
            safe_globals = {"x": x, "exp": exp, "ln": ln, "log": log,
                            "sin": sin, "cos": cos, "tan": tan, 
                            "sec": sec, "csc": csc, "cot": cot}
            
            # Validate and parse inputs
            try:
                integrand = sympify(function_input, locals=safe_globals)
                u = sympify(u_input, locals=safe_globals)
            except SympifyError:
                st.error("Invalid input. Please use valid mathematical syntax (e.g., cos(ln(x))).")
                return

            dv = integrand / u

            # Compute derivatives and integrals
            du = diff(u, x)
            v = integrate(dv, x)

            # Compute the result
            first_term = u * v
            second_term = integrate(v * du, x)
            result = first_term - second_term

            # Display steps
            st.subheader("Step-by-Step Solution")
            
            st.markdown("### 1. Choose u and v':")
            st.latex(f"u = {latex(u)}, \\quad v' = {latex(dv)}")
            
            st.markdown("### 2. Compute du and v:")
            st.latex(f"du = \\frac{{d}}{{dx}}[{latex(u)}] = {latex(du)}")
            st.latex(f"v = \\int {latex(dv)} \\, dx = {latex(v)}")
            
            st.markdown("### 3. Apply the Integration by Parts Formula:")
            st.latex(
                f"\\int {latex(integrand)} \\, dx = u \\cdot v - \\int v \\cdot du"
            )
            st.latex(
                f"= ({latex(u)})({latex(v)}) - \\int ({latex(v)})({latex(du)}) \\, dx"
            )
            
            st.markdown("### 4. Evaluate the Terms:")
            st.latex(f"First Term = {latex(first_term)}")
            st.latex(f"Second Term = \\int {latex(v * du)} \\, dx = {latex(second_term)}")
            
            st.markdown("### 5. Combine Results:")
            st.latex(f"\\int {latex(integrand)} \\, dx = {latex(result)} + C")

            # Final output
            st.subheader("Final Answer")
            st.latex(f"{latex(result)} + C")

        except Exception as e:
            st.error(f"An error occurred: {e}")

# Run the app
if __name__ == "__main__":
    main()