SE3::exp() already does on-manifold integration?

[scott-robotics]

The exp() already applies the tangent on the manifold, as far I understand. So the following,

    auto motion_model = [](const Eigen::Vector2d &integrated_controls) {
        Sophus::SE3d::Tangent dx = Sophus::SE3d::Tangent::Zero();
        const double &displacement = integrated_controls(0);
        const double &theta = integrated_controls(1);
        dx(0) = displacement * std::sin(theta) / (theta + epsilon);
        dx(1) = displacement * (1.0 - std::cos(theta)) / (theta + epsilon);
        dx(5) = theta;
        return Sophus::SE3d::exp(dx);
    };

should just become:

    auto motion_model = [](const Eigen::Vector2d &integrated_controls) {
        Sophus::SE3d::Tangent dx = Sophus::SE3d::Tangent::Zero();
        dx(0) = integrated_controls(0);
        dx(5) = integrated_controls(1);
        return Sophus::SE3d::exp(dx);
    };

?